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# Triangles, Theorems and Proofs: Help and Review Chapter Exam

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!

### Page 1

#### Question 1 1. Find the measure of XZ:

#### Question 2 2. The hypotenuse leg theorem is only applicable with which of the following types of triangles?

#### Question 3 3. If the pictured triangles are congruent, what reason can be given?

#### Question 4 4. If the pictured triangles are congruent, what reason can be given?

#### Question 5 5. Triangle HYV and triangle AYB are similar by the AA similarity theorem. What is the value of x?

### Page 2

#### Question 6 6. Which theorem or postulate can be used to establish congruence with the pictured triangles?

#### Question 7 7. How can we explain that the pictured triangles are congruent?

#### Question 8 8. If triangle MNO is congruent to triangle STR, what must also be true?

#### Question 9 9. You are given that angle B and E are right angles and that the hypotenuses of the triangles are congruent. Which of these is additional information that will help you prove that triangle ABC is congruent to triangle DEF using the HA theorem?

#### Question 10 10. The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is:

### Page 3

#### Question 11 11. In the pictured triangle, AD is an angle bisector. What is the length of AC?

#### Question 12 12. Which theorem can be used to establish congruence with the pictured triangles?

#### Question 13 13. All of the following statements about the pictured triangle must be true, EXCEPT:

#### Question 14 14. If two angles of a triangle are congruent, then which of the following statements must be true?

#### Question 15 15. Brad places a marker on the ground 10 ft. away from the base of a tree at a botanical garden. He walks back towards the tree until he is standing 4 ft. away from the marker, and he is 6 ft. tall. Assuming that the top of Brad's head, the top of the tree, and the marker form two simliar triangles, how tall is the tree?

### Page 4

#### Question 16 16. AD is a perpendicular bisector. Find the measure of AC:

#### Question 17 17. If two sides of a triangle are congruent, then which of the following statements MUST be true?

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

#### Question 19 19. In the pictured triangle, FE is an angle bisector. What is the length of GE?

#### Question 20 20. Given triangles DAR and KMR. What is the value of y?

### Page 5

#### Question 21 21. The hypothesis of a conditional statement:

#### Question 22 22. Which theorem or postulate can be used to establish congruence with the pictured triangles?

#### Question 23 23. Which statement about the pictured triangle must be true?

#### Question 24 24. Triangle ABC is congruent to triangle XYZ. What reason can we use to explain why angle A is congruent to angle X?

#### Question 25 25. Which theorem or postulate can be used to establish congruence with the pictured triangles?

### Page 6

#### Question 26 26. The converse of a conditional statement:

#### Question 27 27. If triangle MNO is congruent to triangle PQR, CPCTC explains which of the following statements?

#### Question 28 28. In the pictured triangles, what reason can we use to explain that angle QPR is congruent to angle SPT?

#### Question 29 29. Greg is standing next to a 40 ft. tree. The sun casts a 5 ft. shadow of Greg, who is 6.4 ft. tall. How long is the tree's shadow?

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

#### Triangles, Theorems and Proofs: Help and Review Chapter Exam Instructions

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