# High School Geometry: Triangles, Theorems and Proofs Chapter Exam

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#### Question 1 1. Brad places a mirror on the ground 10 ft. away from the base of a bush at a botanical garden. He walks back towards the bush until he can see the top of the bush in the mirror. If Brad is standing 4 ft. away from the mirror, and is 6 ft. tall, how tall is the bush?

#### Question 2 2. If the pictured triangles are congruent, what reason can be given?

#### Question 3 3. In the pictured triangles, what reason can we use to explain that angle QPR is congruent to angle SPT?

#### Question 4 4. Triangle ABC is congruent to triangle XYZ. What reason can we use to explain why angle A is congruent to angle X?

#### Question 5 5. Which theorem or postulate can be used to establish congruence with the pictured triangles?

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#### Question 6 6. If the pictured triangles are congruent, what reason can be given?

#### Question 7 7. If the pictured triangles are congruent, what reason can be given?

#### Question 8 8. The conclusion of a conditional statement:

#### Question 9 9. Which theorem can be used to establish congruence with the pictured triangles?

#### Question 10 10. Study the given diagram. Find the value of x, the distance between T and E.

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#### Question 11 11. Given triangles DAR and KMR. What is the value of y?

#### Question 12 12. If triangle MNO is congruent to triangle STR, what must also be true?

#### Question 13 13. The hypotenuse leg theorem is only applicable with which of the following types of triangles?

#### Question 14 14. What additional information do you need to prove that triangle ABC is congruent to triangle DEF using the HA theorem?

#### Question 15 15. Triangle HYV and triangle AYB are similar by the AA similarity theorem. What is the value of x?

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#### Question 16 16. Find the measure of MN:

#### Question 17 17. The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is:

#### Question 18 18. If the pictured triangles are congruent, what reason can be given?

#### Question 19 19. Which theorem or postulate can be used to establish congruence with the pictured triangles?

#### Question 20 20. Which of the following represents the angle bisector theorem for the pictured triangle?

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#### Question 21 21. How can we explain that the pictured triangles are congruent?

#### Question 22 22. All of the following statements about the pictured triangle must be true, EXCEPT:

#### Question 23 23. The hypotenuse angle theorem is only applicable with which of the following types of triangles?

#### Question 24 24. The AAS theorem requires which of the following to be congruent?

#### Question 25 25. In the pictured triangle, MS is an angle bisector. What is the length of SO?

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#### Question 26 26. If the pictured triangles are congruent, what reason can be given?

#### Question 27 27. The converse of the perpendicular bisector theorem states that:

#### Question 28 28. What additional information do you need to be given to prove that triangle PQS is congruent to triangle SRP using the HA theorem?

#### Question 29 29. If two angles of a triangle are congruent, then which of the following statements must be true?

#### Question 30 30. Which theorem can be used to establish congruence with the pictured triangles?

#### High School Geometry: Triangles, Theorems and Proofs Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!