Download Ch. 4 Review

Name______________________________________________Per______________Date____________________________ Geometry Ch. 4 Review Find the measures of the sides of ΔMNP and classify the triangle by its sides. 1. M(-­‐3,2), N(2,1), P(-­‐2,-­‐3) 2. M(5,-­‐3), N(3,4), P(-­‐1,1) Is there enough information to determine triangle congruency. Determine how you can prove congruency (ASA, SSS, etc). 3. 5. 4. 6.
8. Write a triangle congruence statement, name the congruent angles and sides. 7. Find the measure of each angle. 58° 1 39° 55° 2 3 9. ΔABC ≅ Δ______.
10. If BCDE is congruent to OPQR, then
11. If
a.
is congruent to
, which of the following can you NOT conclude as being true?
b.
c.
d.
12. The two triangles are congruent as suggested by their appearance. Find the value of c. The
diagrams are not to scale.
13. Given
and
14. Given
, find the length of QS and TV.
and
15. What other information do you need in order
to prove the triangles congruent using the
SAS Congruence Postulate?
17. From the information in the diagram,
can you prove ΔFDG ≅ ΔFDE ?
€
, find
and
16. Name the angle included by the sides
and
18. For which situation could you prove
using the HL Theorem?
19. Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that
20. Triangle ABC is an equilateral triangle.
AD bisects ∠BAC . DC = 6x, AB = 8x+12,
and ∠BAD = 3y. Find x and y.
.
21. Find the values of x and y.
22. What is the measure of a base angle of an isosceles triangle if the vertex angle measures
38° and the two congruent sides each measure 21 units?
23. Triangle MNP is an isosceles triangle. M N ≅ NP . NP = 2x+20, M N=5x+5, and P M=8x-2.
Find x and the measure of each side of the triangle.
24. The measure of the angles of ΔJKL are 18x-12, 10x+20, and 15x. Draw a figure to
illustrate ΔJKL, find x, and the measure of each angle.
25. What is the measure of the vertex angle of an isosceles triangle if one of its base
angles measures 42°?
26. In an A-frame house, the two congruent sides extend from the ground to form a 34° angle
at the peak. What angle does each side form with the ground?
27. Find the value of x.
28. Find the value of x. Diagram is not to scale.
The diagram is not to scale.
Given:
,