SAT Math Flashcards: Lines Angles And Triangles

What this deck covers

This deck focuses on Lines Angles And Triangles, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the exterior angle theorem for triangles?

Answer: Exterior angle = sum of two remote interior angles. An exterior angle equals the sum of the two non-adjacent interior angles.

Flashcard 2: What is the measure of each angle in an equilateral triangle?

Answer: 60 degrees. Since all angles are equal and sum to $180°$, each is $180° ÷ 3 = 60°$.

Flashcard 3: What is the measure of an angle in an equilateral triangle?

Answer: 60 degrees. Each angle in an equilateral triangle measures $180° ÷ 3 = 60°$.

Flashcard 4: What is the sum of the exterior angles of a triangle?

Answer: 360 degrees. The exterior angles of any polygon always sum to $360°$.

Flashcard 5: What is the sum of the interior angles of a triangle?

Answer: 180 degrees. This is a fundamental property of all triangles in Euclidean geometry.

Flashcard 6: What is the formula to find the perimeter of a triangle?

Answer: Sum of all sides. Add the lengths of all three sides together.

Flashcard 7: What is the term for a triangle with one angle greater than 90°?

Answer: Obtuse triangle. Contains one angle greater than $90°$ but less than $180°$.

Flashcard 8: Identify the type of angles that sum up to 180 degrees.

Answer: Supplementary angles. Two angles whose measures add up to $180°$.

Flashcard 9: Calculate the measure of an exterior angle of a regular hexagon.

Answer: 60 degrees. Each exterior angle of a regular hexagon: $360° ÷ 6 = 60°$.

Flashcard 10: State the relationship between vertical angles.

Answer: They are equal. Vertical angles are formed when two lines intersect and are always congruent.

Flashcard 11: What is the sum of the interior angles of a triangle?

Answer: 180 degrees. This is a fundamental property of all triangles in Euclidean geometry.

Flashcard 12: Identify the formula for the area of a triangle.

Answer: Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Multiply base by height, then divide by 2 for triangle area.

Flashcard 13: Find the missing angle in a triangle with angles 40° and 80°.

Answer: 60 degrees. Triangle angles sum to $180°$: $40° + 80° + x = 180°$.

Flashcard 14: What property do the base angles of an isosceles triangle have?

Answer: Base angles are equal. The two angles opposite the equal sides are congruent.

Flashcard 15: Identify the type of angles that sum up to 90 degrees.

Answer: Complementary angles. Two angles whose measures add up to $90°$.

Flashcard 16: What is the sum of the angles in a quadrilateral?

Answer: 360 degrees. Any quadrilateral's interior angles sum to $360°$.

Flashcard 17: State the Pythagorean theorem for right triangles.

Answer: $a^2 + b^2 = c^2$. Relates the squares of the legs to the square of the hypotenuse.

Flashcard 18: Identify the type of angles that sum up to 180 degrees.

Answer: Supplementary angles. Two angles whose measures add up to $180°$.

Flashcard 19: What is the relationship of angles in parallel lines cut by a transversal?

Answer: Alternate interior angles are equal. When parallel lines are cut by a transversal, alternate interior angles are congruent.

Flashcard 20: Which type of angle measures greater than 90 degrees?

Answer: Obtuse angle. Measures between $90°$ and $180°$, larger than a right angle.

Flashcard 21: Identify the type of triangle with all sides equal.

Answer: Equilateral triangle. All three sides have the same length.

Flashcard 22: What is the characteristic of an isosceles triangle?

Answer: Two sides of equal length. Has exactly two sides of equal length and two equal angles.

Flashcard 23: What is the sum of the exterior angles of a triangle?

Answer: 360 degrees. The exterior angles of any polygon always sum to $360°$.

Flashcard 24: What is the sum of the interior angles of a triangle?

Answer: 180 degrees. This is a fundamental property that applies to all triangles.

Flashcard 25: Which angle is opposite the hypotenuse in a right triangle?

Answer: The right angle (90 degrees). The largest angle is always opposite the longest side (hypotenuse).

Flashcard 26: What is the relationship between vertical angles?

Answer: Vertical angles are congruent. Opposite angles formed by intersecting lines are always equal.

Flashcard 27: Calculate the area of a right triangle with legs of 6 and 8.

Answer: 24 square units. Area = $\frac{1}{2} \times 6 \times 8 = 24$ square units.

Flashcard 28: What do you call a triangle with all angles less than 90°?

Answer: Acute triangle. All three angles measure less than $90°$.

Flashcard 29: State the Pythagorean theorem for right triangles.

Answer: $a^2 + b^2 = c^2$. Relates the squares of the legs to the square of the hypotenuse.

Flashcard 30: Calculate the missing angle: 45°, 55°, and ? in a triangle.

Answer: 80 degrees. Sum of triangle angles is $180°$: $180° - 45° - 55° = 80°$.

Flashcard 31: Find the value of $x$ if two angles of a triangle are 50° and 60°.

Answer: $x = 70$ degrees. Triangle angles sum to $180°$: $50° + 60° + x = 180°$.

Flashcard 32: Identify a triangle with one angle equal to 90 degrees.

Answer: Right triangle. Contains exactly one $90°$ angle with two acute angles.

Flashcard 33: Which type of triangle has all equal sides?

Answer: Equilateral triangle. All three sides congruent means all angles are $60°$ each.

Flashcard 34: Find the missing angle if two angles of a triangle are 70° and 50°.

Answer: 60 degrees. Triangle angles sum to $180°$: $180° - 70° - 50° = 60°$.

Flashcard 35: What do you call a triangle with all angles less than 90°?

Answer: Acute triangle. All three angles measure less than $90°$.

Flashcard 36: Identify the property of vertically opposite angles.

Answer: They are equal. Angles formed by intersecting lines across from each other are congruent.

Flashcard 37: Identify the property of vertically opposite angles.

Answer: They are equal. Angles formed by intersecting lines across from each other are congruent.

Flashcard 38: Find the length of the longer leg in a 30-60-90 triangle with hypotenuse 10.

Answer: $5\sqrt{3}$. In a 30-60-90 triangle, longer leg = hypotenuse × $\frac{\sqrt{3}}{2}$.

Flashcard 39: What is the sum of the interior angles of a triangle?

Answer: 180 degrees. This is a fundamental property of all triangles.

Flashcard 40: What is the sum of the exterior angles of any polygon?

Answer: 360 degrees. This applies to all polygons, regardless of number of sides.

Flashcard 41: What is the sum of the interior angles of a triangle?

Answer: 180 degrees. This is a fundamental property that applies to all triangles.

Flashcard 42: What is the relationship between vertical angles?

Answer: Vertical angles are congruent. Opposite angles formed by intersecting lines are always equal.

Flashcard 43: Identify the type of triangle with angles measuring 45°, 45°, and 90°.

Answer: Isosceles right triangle. Has two $45°$ angles and one $90°$ angle with two equal legs.

Flashcard 44: What is the definition of an isosceles triangle?

Answer: A triangle with two equal sides. Two equal sides create two equal base angles in the triangle.

Flashcard 45: State the formula for the area of a right triangle.

Answer: $\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2$. The two legs are perpendicular, so multiply and divide by 2.

Flashcard 46: What is the formula for the Pythagorean theorem?

Answer: $a^2 + b^2 = c^2$. Relates the sides of a right triangle: legs squared equal hypotenuse squared.

Flashcard 47: Identify the relationship between corresponding angles in parallel lines.

Answer: They are equal. When parallel lines are cut by a transversal, corresponding angles are congruent.

Flashcard 48: What is the measure of each angle in an equilateral triangle?

Answer: 60 degrees. Since all angles are equal and sum to $180°$, each is $180° ÷ 3 = 60°$.

Flashcard 49: State the formula for the area of a triangle.

Answer: Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Standard formula using base and perpendicular height.

Flashcard 50: What is the sum of the interior angles of a triangle?

Answer: 180 degrees. This is a fundamental property of all triangles.

Flashcard 51: Find the third angle of a triangle given 30° and 60°.

Answer: 90 degrees. Triangle angles sum to $180°$: $180° - 30° - 60° = 90°$.

Flashcard 52: What is the Pythagorean Theorem?

Answer: $a^2 + b^2 = c^2$. Relates the sides of a right triangle: legs squared equal hypotenuse squared.

Flashcard 53: Identify the term for a triangle with all sides equal.

Answer: Equilateral triangle. All three sides are equal in length and all angles are $60°$.

Flashcard 54: Identify the relationship between corresponding angles in parallel lines.

Answer: They are equal. When parallel lines are cut by a transversal, corresponding angles are congruent.

Flashcard 55: What is the formula for the Pythagorean theorem?

Answer: $a^2 + b^2 = c^2$. Relates the sides of a right triangle: legs squared equal hypotenuse squared.

Flashcard 56: Identify the type of triangle with angles measuring 30°, 60°, and 90°.

Answer: Special right triangle. Has angle measures in the ratio $1:2:3$ or $30°:60°:90°$.

Flashcard 57: Identify a triangle with one angle equal to 90 degrees.

Answer: Right triangle. Contains exactly one $90°$ angle with two acute angles.

Flashcard 58: State the relationship between vertical angles.

Answer: They are equal. Vertical angles are formed when two lines intersect and are always congruent.

Flashcard 59: Calculate the measure of an exterior angle of a regular hexagon.

Answer: 60 degrees. Each exterior angle of a regular hexagon: $360° ÷ 6 = 60°$.

Flashcard 60: State the formula for the area of a triangle.

Answer: $\frac{1}{2} \times \text{base} \times \text{height}$. Multiply base by height, then divide by 2.

Flashcard 61: Find the length of the hypotenuse in a 45-45-90 triangle with legs of 7.

Answer: $7\text{√2}$. In 45-45-90 triangles, hypotenuse = leg × $\sqrt{2}$.

Flashcard 62: What is the term for a triangle with one angle greater than 90°?

Answer: Obtuse triangle. Contains one angle greater than $90°$ but less than $180°$.

Flashcard 63: What is the sum of the exterior angles of any polygon?

Answer: 360 degrees. This applies to all polygons, regardless of number of sides.

Flashcard 64: Find the length of the longer leg in a 30-60-90 triangle with hypotenuse 10.

Answer: $5\sqrt{3}$. In a 30-60-90 triangle, longer leg = hypotenuse × $\frac{\sqrt{3}}{2}$

Flashcard 65: State the formula for the sum of interior angles of a polygon.

Answer: Sum = $(n-2) \times 180$ degrees. For $n$ sides, subtract 2 then multiply by $180°$.

Flashcard 66: What is the measure of an angle in an equilateral triangle?

Answer: 60 degrees. Each angle in an equilateral triangle measures $180° ÷ 3 = 60°$.

Flashcard 67: What is the relationship of angles in parallel lines cut by a transversal?

Answer: Alternate interior angles are equal. When parallel lines are cut by a transversal, alternate interior angles are congruent.

Flashcard 68: Find the length of the hypotenuse in a 45-45-90 triangle with legs of 7.

Answer: $7\text{√2}$. In 45-45-90 triangles, hypotenuse = leg × $\sqrt{2}$.

Flashcard 69: Identify the type of angles formed by two intersecting lines.

Answer: Vertical angles. Opposite angles formed when two lines intersect are called vertical angles.

Flashcard 70: What is a line that divides an angle into two equal parts called?

Answer: Angle bisector. Divides an angle into two congruent angles.

Flashcard 71: State the formula for the area of a triangle.

Answer: $\frac{1}{2} \times \text{base} \times \text{height}$. Multiply base by height, then divide by 2.

Flashcard 72: State the formula for the sum of interior angles of a polygon.

Answer: Sum = $(n-2) \times 180$ degrees. For $n$ sides, subtract 2 then multiply by $180°$.

Flashcard 73: Identify the type of triangle with a 90° angle.

Answer: Right triangle. Contains exactly one $90°$ angle.

Flashcard 74: What is the definition of a right triangle?

Answer: A triangle with one 90-degree angle. The right angle distinguishes it from acute and obtuse triangles.

Flashcard 75: What is the formula to find the perimeter of a triangle?

Answer: Sum of all sides. Add the lengths of all three sides together.

Flashcard 76: What is the term for a line segment connecting two non-adjacent vertices of a polygon?

Answer: Diagonal. Connects two vertices that are not adjacent (next to each other).

Flashcard 77: What is the term for a straight path extending infinitely in both directions?

Answer: Line. Has no endpoints and extends infinitely in both directions.

Flashcard 78: Identify the type of angles that sum up to 90 degrees.

Answer: Complementary angles. Two angles whose measures add up to $90°$.

Flashcard 79: What is the name of a line segment from a vertex to the midpoint of the opposite side?

Answer: Median. Connects a vertex to the midpoint of the opposite side.

Flashcard 80: Which type of angle measures greater than 90 degrees?

Answer: Obtuse angle. Measures between $90°$ and $180°$, larger than a right angle.

Flashcard 81: Identify the type of triangle with angles measuring 45°, 45°, and 90°.

Answer: Isosceles right triangle. Has two $45°$ angles and one $90°$ angle with two equal legs.

Flashcard 82: What is the sum of angles in any triangle?

Answer: 180 degrees. This is a fundamental property of triangles in Euclidean geometry.

Flashcard 83: Identify the type of triangle with angles measuring 30°, 60°, and 90°.

Answer: Special right triangle. Has angle measures in the ratio $1:2:3$ or $30°:60°:90°$.

Flashcard 84: What is the term for a straight path extending infinitely in both directions?

Answer: Line. Has no endpoints and extends infinitely in both directions.

Flashcard 85: Calculate the area of a right triangle with legs of 6 and 8.

Answer: 24 square units. Area = $\frac{1}{2} \times 6 \times 8 = 24$ square units.

Flashcard 86: What is the name of a line segment from a vertex to the midpoint of the opposite side?

Answer: Median. Connects a vertex to the midpoint of the opposite side.

Flashcard 87: What property do the base angles of an isosceles triangle have?

Answer: Base angles are equal. The two angles opposite the equal sides are congruent.

Flashcard 88: What is the definition of an isosceles triangle?

Answer: A triangle with two equal sides. Two equal sides create two equal base angles in the triangle.

Flashcard 89: What is the relationship between consecutive interior angles on parallel lines?

Answer: They are supplementary. Consecutive interior angles on the same side of a transversal sum to $180°$.

Flashcard 90: Find the third angle of a triangle if two angles are 45° and 55°.

Answer: 80 degrees. Triangle angles sum to $180°$: $180° - 45° - 55° = 80°$.

Flashcard 91: What is the term for two angles that share a common side and vertex?

Answer: Adjacent angles. Share a common vertex and a common side but no interior points.

Flashcard 92: What is the exterior angle theorem for triangles?

Answer: Exterior angle = sum of two remote interior angles. An exterior angle equals the sum of the two non-adjacent interior angles.

Flashcard 93: Which type of triangle has all equal sides?

Answer: Equilateral triangle. All three sides congruent means all angles are $60°$ each.

Flashcard 94: Which theorem states the sum of angles in a triangle is constant?

Answer: Triangle Sum Theorem. States that interior angles of any triangle sum to $180°$.

Flashcard 95: Identify the name of a triangle with no equal sides.

Answer: Scalene triangle. All three sides have different lengths.

Flashcard 96: Identify the formula for the area of a triangle.

Answer: Area = $\frac{1}{2} \times \text{base} \times \text{height}$. Multiply base by height, then divide by 2 for triangle area.

Flashcard 97: Find the third angle of a triangle if two angles are 45° and 55°.

Answer: 80 degrees. Triangle angles sum to $180°$: $180° - 45° - 55° = 80°$.

Flashcard 98: Find the length of the hypotenuse with legs 3 and 4.

Answer: 5 units. Using Pythagorean theorem: $\sqrt{3^2 + 4^2} = \sqrt{25} = 5$.

Flashcard 99: What is a line that divides an angle into two equal parts called?

Answer: Angle bisector. Divides an angle into two congruent angles.

Flashcard 100: What is the definition of a right triangle?

Answer: A triangle with one 90-degree angle. The right angle distinguishes it from acute and obtuse triangles.