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Name: ______________________________
Date: ________ Block: _____
Geometry Chapter 4 Review
Find the value of x. Then classify the triangle by its angles.
1.
2.
3.
x = __________
x = __________
x = __________
classify: _______
classify: _________
(x + 12)°
classify: _________
4.
x = _________
classify: _________
Complete the congruence statement for the figures.
5. ABCD ≅ ______
State the congruence that is needed to prove ∆ABC ≅ ∆DEF using the given postulate
or theorem.
6. Given: BC  EF ; Use the Hypotenuse-Leg Congruence Theorem
7. Given: AB  DE , AC  DF ; Use the SSS Congruence Postulate
8. Given: ∠A ≅ ∠D, ∠B ≅ ∠E; Use the AAS Congruence Theorem
9. Given: ∠A ≅ ∠D, ∠C ≅ ∠F; Use the ASA Congruence Postulate
Decide whether the triangles can be proven congruent by the given postulate or
theorem.
10. ∆TWX ≅ ∆YWX by SSS
yes / no
Find the value of x.
11.
12.
5x - 2
x = __________________
3x + 8
x = ___________________
Use the diagram to find the measure.
13. m∠ WYX = _____
14. WX = _____
Is it possible to prove ∆ABC ≅ ∆DEF using the given information? If so, state the
postulate or theorem you would use.
15. AB  DE , AC  DF , BC  EF
16. ∠A ≅ ∠D, AB  DE , BC  EF
17. ∠A ≅ ∠D, ∠C ≅ ∠F, ∠B ≅ ∠E
18. ∠A ≅ ∠D, ∠C ≅ ∠F, BC  EF
Part 2 of Chapter 4 Review
#1-3. Classify the following triangles by the number of sides.
1) ________________
2) _________________
3) _________________
#4-6. Classify the following triangles by their angles.
4) ________________
5) _________________
6) _________________
#7-8. Given: AB  BC
7) Solve for x.
equilateral?
8) Is the triangle
9) How many obtuse angles can an isosceles triangle have? __________
10) In ABC, AB  BC . Which term does not describe the triangle?
a)
b)
c)
d)
acute
isosceles
equilateral
obtuse
11) In a right triangle, the side across from the right angle is called the
___________________.
12) ABC  DEF. Also AB  EF . What type of triangle is ABC?
_______________________
(Hint: Draw both triangles!)
#13-15. Find the measures of the numbered angles.
13) m1 = ___________
14) m2 = ___________
15) m3 = ___________
16) Find the measure of BCD.
mBCD = __________
#17-19. Find the measures of A, B, and C.
17) mA = ________
18) mB = ________
19) mC = ________
20) Refer to the figure on
the right. mA= ________.
21) The measure of B is_________.
#22-24. What are the values of x, y, and z?
22) x = _________
23) y = _________
24) z = _________
#25-27. In ∆ABC, A  C and
B is a right angle.
Find the measure of each angle.
25) mA = __________
26) mB = __________
27) mC = __________
#28-29. Find the value of y.
28) y = _____________
29) y = ______________
#30-32. In the diagram, ∆TJM  ∆PHS. Complete the statements below.
30)
P  ___________
31) mM  ___________
32) ∆HPS  ___________
33) State two methods (i.e. SSS, SAS, ASA, AAS, or HL)
that can be used to conclude that
AOB  COD.
Method 1: __________
Method 2: __________
34) Given AB  DE and B  E,
what would you use to prove
that ABC  DEC (SSS, SAS,
ASA, AAS, or HL)?
Answer: ___________
35) Given BAC  DAC and B  D,
what would you use to prove that
ABC  ADC (SSS, SAS, ASA, AAS, or HL)?
Answer: ______________
36) ABD  CBD. Name the theorem or
postulate (ex. SSS, SAS, ASA, AAS,
or HL) that justifies the congruence.
Answer: ______________
#37-40. Tell which method(s) you can use to prove that the triangles are congruent.
If no method can be used, write “none”.
37.
Answer: ___________
38.
Answer: ___________
39.
Answer: ___________
40.
Answer: ___________