Question

math 2 unit 2 test congruence - version 1
name: thiago gonzalez
matching: use the figure below to classify each pair of angles using the vocabulary to the right. answers may be used more than once.
a. corresponding angles
b. same - side exterior angles
c. vertical angles
d. linear pairs
e. none of these angle pairs

1. ∠4 and ∠5 2. ∠6 and ∠8 3. ∠2 and ∠3
2. ∠3 and ∠5 5. ∠1 and ∠4
3. which of the following is not a postulate used to prove the congruence of two triangles?

a. asa b. ssa c. sas d. sss

1. if △igh≅△klj, then ∠h is congruent to

a. ∠j b. ∠i c. ∠k d. ∠l

1. if △xyz≅△def, then (overline{de}) is congruent to

a. (overline{xy}) b. (overline{ef}) c. (overline{yz}) d. (overline{fd})

Explanation:

Step1: Identify angle - pair types

For ∠4 and ∠5, they are vertical angles (opposite angles formed by the intersection of two lines), so the answer is C.

Step2: Analyze ∠6 and ∠8

∠6 and ∠8 are vertical angles, so the answer is C.

Step3: Examine ∠2 and ∠3

∠2 and ∠3 are a linear - pair (adjacent angles that form a straight line), so the answer is D.

Step4: Look at ∠3 and ∠5

∠3 and ∠5 are same - side interior angles, not in the given options, so the answer is E.

Step5: Consider ∠1 and ∠4

∠1 and ∠4 are corresponding angles, so the answer is A.

Step6: Recall triangle - congruence postulates

ASA (Angle - Side - Angle), SAS (Side - Angle - Side), and SSS (Side - Side - Side) are valid postulates for triangle congruence. SSA is not a valid postulate as it does not always guarantee congruence. So the answer is B.

Step7: Use congruent - triangle angle correspondence

If ΔIGH≅ΔKLJ, corresponding angles are congruent. ∠H corresponds to ∠J. So the answer is A.

Step8: Apply congruent - triangle side correspondence

If ΔXYZ≅ΔDEF, corresponding sides are congruent. \(\overline{DE}\) corresponds to \(\overline{XY}\). So the answer is A.

Answer:

1. C
2. C
3. D
4. E
5. A
6. B
7. A
8. A