Prove Geometric Theorems: Lines and Angles
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Geometry › Prove Geometric Theorems: Lines and Angles
Which of the following describes 
These are vertically opposite angles, therefore they are equal
These are vertically opposite angles, there is not enough information to determine any further relation
These are corresponding angles, therefore they are equal
These are corresponding angles, there is not enough information to determine any further relation
Explanation
To answer this question, we must understand the definition of vertically opposite angles. Vertically opposite angles are angles that are formed opposite of each other when two lines intersect. Vertically opposite angles are always congruent to each other.
Which of the following describes
These are vertically opposite angles, therefore they are equal
These are vertically opposite angles, there is not enough information to determine any further relation
These are corresponding angles, therefore they are equal
These are corresponding angles, there is not enough information to determine any further relation
Explanation
To answer this question, we must understand the definition of vertically opposite angles. Vertically opposite angles are angles that are formed opposite of each other when two lines intersect. Vertically opposite angles are always congruent to each other.
True or False: The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal then the pair of corresponding angles are supplementary.
True
False
Explanation
The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal line then the pair of corresponding angles are congruent. Corresponding angles are angles formed when a transversal line cuts two lines and they lie in the same position at each intersection. The figure below illustrates corresponding lines.
True or False: The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal then the pair of corresponding angles are supplementary.
True
False
Explanation
The Corresponding Angles Theorem states that if two parallel lines are cut by a transversal line then the pair of corresponding angles are congruent. Corresponding angles are angles formed when a transversal line cuts two lines and they lie in the same position at each intersection. The figure below illustrates corresponding lines.
Which of the following describes 
These angles are complementary angles, therefore they sum to 90
These angles are corresponding angles, therefore they are equal
These angles are alternate exterior angles, therefore they are equal
These angles are alternate interior angles, therefore they are equal
Explanation
To answer this question, we must understand the definition of alternate exterior angles. When a transversal line intersects two parallel lines, 4 exterior angles are formed. Alternate exterior angles are angles on the outsides of these two parallel lines and opposite of each other.
Which of the following describes
These angles are complementary angles, therefore they sum to 90
These angles are corresponding angles, therefore they are equal
These angles are alternate exterior angles, therefore they are equal
These angles are alternate interior angles, therefore they are equal
Explanation
To answer this question, we must understand the definition of alternate exterior angles. When a transversal line intersects two parallel lines, 4 exterior angles are formed. Alternate exterior angles are angles on the outsides of these two parallel lines and opposite of each other.
True or False: Lines AB and CD are parallel.
True
False
Explanation
We know that lines AB and CD are parallel due to the information we get from the angles formed by the transversal line. There are:
- two pairs of congruent vertically opposite angles
- two pairs of congruent alternate interior angles
- two pairs of congruent alternate exterior angles
- two pairs of congruent corresponding angles
Just using any one of these facts is enough proof that lines AB and CD are parallel.
True or False: Lines AB and CD are parallel.
True
False
Explanation
We know that lines AB and CD are parallel due to the information we get from the angles formed by the transversal line. There are:
- two pairs of congruent vertically opposite angles
- two pairs of congruent alternate interior angles
- two pairs of congruent alternate exterior angles
- two pairs of congruent corresponding angles
Just using any one of these facts is enough proof that lines AB and CD are parallel.
What does it mean for two angles to be complementary angles?
Complementary angles are any two angles in a triangle that sum to be 90
Complementary angles are any two angles that sum to be 90
Complementary angles are any two angles that sum to be 180
Complementary angles are any two angles in a triangle that sum to be 180
Explanation
The definition of complementary angles is: any two angles that sum to 90. We most often see these angles as the two angles in a right triangle that are not the right angle. These two angles do not have to only be in right triangles, however. Complementary triangles are any pair of angles that add up to be 90.
What does it mean for two angles to be complementary angles?
Complementary angles are any two angles in a triangle that sum to be 90
Complementary angles are any two angles that sum to be 90
Complementary angles are any two angles that sum to be 180
Complementary angles are any two angles in a triangle that sum to be 180
Explanation
The definition of complementary angles is: any two angles that sum to 90. We most often see these angles as the two angles in a right triangle that are not the right angle. These two angles do not have to only be in right triangles, however. Complementary triangles are any pair of angles that add up to be 90.