Geometry Chapter 4 Practice Problems
1. Find the value of x:
2. Refer to the figure below. .
3. What is the value of z? (The figure may not be drawn to scale.)
4. Solve for x, given that . Is equilateral?
5. Given: , ÐB @ ÐD
Prove:
6. If , and , which of the following statements is false?
a. / c.b. / d.
7. If which statement is NOT true?
a. / c.b. / d.
8. If , then @ .
9. Given: ; ; C is the midpoint of and
Prove: DABC @ DEDC
10. Refer to the figure below. .
Use the diagram to decide whether the congruence statement is true. Explain your reasoning.
11.
12.
13.
14. Given:
Prove: D @ D
Would HL, ASA, SAS, AAS, or SSS be used to justify that the pair of triangles is congruent?
15.
16.
17.
18.
19. Performance Task: Is there enough information given to prove that the following pairs of triangles are congruent? Explain why or why not. If not, describe what information could be added to guarantee congruence.
20.
21. Find the values of x and y.
22.
23. SHORT RESPONSE Write your answer on a separate piece of paper.
Triangle RST is isosceles, with and (The figure may not be drawn to scale.)
Part A Write an equation that can be solved to find the value of x. Explain the origin of the equation.
Part B Solve the equation in Part A and use the answer to find the measure, in degrees, of
24. Given:
Prove: is isosceles
25. . Also . What type of triangle is ? Explain.
Geometry Chapter 4 Practice Problems
Answer Section
1. 31°
2. 17°
3.
4. x = 5; yes
5.
Statements / Reasons1. / 1. Given
2. / 2. Given
3. mÐBAC + mÐB + mÐBCA = 180°
mÐDAC + mÐD + mÐDCA = 180° / 3. Triangle Sum Theorem
4. mÐBAC + mÐB + mÐBCA = mÐDAC + mÐD + mÐDCA / 4. Transitive Property
5. mÐDAC + mÐD + mÐBCA = mÐDAC + mÐD + mÐDCA / 5. Substitution Property
6. mÐBCA = mÐDCA / 6. Subtraction Property
7. / 7. Symmetric Property of Congruent Angles
6. A
7. B
8.
9.
10.
11. True; SSS Congruence Theorem
12. False; the two triangles in the congruence statement are congruent, but the vertices are out of order, so the statement is false.
13. False; no two pairs of sides of the triangles are congruent.
14.
15. SAS
16. AAS
17. AAS
18. ASA
19. a. No; you either need the pair of included angles to be congruent or the other pair of corresponding sides to be congruent in order to prove the triangles congruent.
b. No; you either need one pair of corresponding acute angles to be congruent or one more pair of corresponding sides to be congruent in order to prove that the triangles are congruent.
c. Yes by SAS
d. Yes by SSS
e. Yes by AAS
f. No; you need one pair of corresponding sides to be congruent in order to prove that the triangles are congruent.
20.
21. x = 12°, y = 84°
22. 60
23. Part A which means that the measure of is . The sum of the measures of and is 180°, because they form a straight angle, so the equation is
Part B
The measure of is .
Alternatively, the measure of is , so = . The measure of is the same as the measure of so = 40°
24.
25. Isosceles. , so . Then, since , by the Transitive Property of Congruence. Therefore, is isosceles.