Lines, Angles, & Triangles - SAT Math

1. What is the measure of each angle in an equilateral triangle?

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

2. What is the sum of the exterior angles of a triangle?

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

3. What is the sum of the interior angles of a triangle?

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

4. What is the formula to find the perimeter of a triangle?

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

5. What is the term for a triangle with one angle greater than 90°?

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

6. Identify the type of angles that sum up to 180 degrees.

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

7. Calculate the measure of an exterior angle of a regular hexagon.

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

8. Identify the formula for the area of a triangle.

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

9. What property do the base angles of an isosceles triangle have?

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

10. Identify the type of angles that sum up to 90 degrees.

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

11. What is the sum of the angles in a quadrilateral?

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

12. State the Pythagorean theorem for right triangles.

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

13. Which type of angle measures greater than 90 degrees?

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

14. Identify the type of triangle with all sides equal.

    Equilateral triangle. All three sides have the same length.

15. What is the characteristic of an isosceles triangle?

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

16. What is the sum of the interior angles of a triangle?

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

17. What is the relationship between vertical angles?

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

18. What do you call a triangle with all angles less than 90°?

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

19. Identify a triangle with one angle equal to 90 degrees.

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

20. Which type of triangle has all equal sides?

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

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

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

22. Identify the property of vertically opposite angles.

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

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

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

24. State the formula for the area of a right triangle.

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

25. What is the formula for the Pythagorean theorem?

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

26. What is the sum of the interior angles of a triangle?

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

27. What is the Pythagorean Theorem?

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

28. Identify the term for a triangle with all sides equal.

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

29. Identify the relationship between corresponding angles in parallel lines.

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

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

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

31. State the relationship between vertical angles.

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

32. What is the sum of the exterior angles of any polygon?

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

33. State the formula for the sum of interior angles of a polygon.

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

34. What is the measure of an angle in an equilateral triangle?

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

35. What is the relationship of angles in parallel lines cut by a transversal?

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

36. Find the length of the hypotenuse in a 45-45-90 triangle with legs of 7.

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

37. Identify the type of angles formed by two intersecting lines.

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

38. What is a line that divides an angle into two equal parts called?

    Angle bisector. Divides an angle into two congruent angles.

39. State the formula for the area of a triangle.

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

40. What is the definition of a right triangle?

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

41. What is the term for a line segment connecting two non-adjacent vertices of a polygon?

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

42. What is the name of a line segment from a vertex to the midpoint of the opposite side?

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

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

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

44. What is the sum of angles in any triangle?

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

45. What is the term for a straight path extending infinitely in both directions?

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

46. Calculate the area of a right triangle with legs of 6 and 8.

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

47. What is the definition of an isosceles triangle?

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

48. What is the relationship between consecutive interior angles on parallel lines?

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

49. What is the exterior angle theorem for triangles?

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

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

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

51. Find the length of the hypotenuse with legs 3 and 4.

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

52. What is the term for two angles that share a common side and vertex?

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

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

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

54. State the formula for the area of a triangle.

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

55. Which angle is opposite the hypotenuse in a right triangle?

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

56. Find the third angle of a triangle given 30° and 60°.

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

57. Identify the name of a triangle with no equal sides.

    Scalene triangle. All three sides have different lengths.

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

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

59. Find the missing angle in a triangle with angles 40° and 80°.

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

60. Identify the type of triangle with a 90° angle.

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

61. Which theorem states the sum of angles in a triangle is constant?

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

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