Question

ii. (continued) state whether these triangles are congruent by asa, aas, or none
7.
8.
9.
10.
11.
12.
iii. state whether these triangles are congruent by hl, if not write no.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

Explanation:

Step1: Recall congruence criteria

ASA (Angle - Side - Angle) means two angles and the included side of one triangle are equal to two angles and the included side of another triangle. AAS (Angle - Angle - Side) means two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle. HL (Hypotenuse - Leg) is for right - angled triangles where the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle.

Step2: Analyze II.7

Check for ASA or AAS. There are two angles and the included side marked equal, so it is congruent by ASA.

Step3: Analyze II.8

There are two angles and the included side marked equal, so it is congruent by ASA.

Step4: Analyze II.9

There are two angles and a non - included side marked equal, so it is congruent by AAS.

Step5: Analyze II.10

There are two angles and the included side marked equal, so it is congruent by ASA.

Step6: Analyze II.11

There are two angles and the included side marked equal, so it is congruent by ASA.

Step7: Analyze II.12

There are two angles and a non - included side marked equal, so it is congruent by AAS.

Step8: Analyze III.1

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step9: Analyze III.2

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step10: Analyze III.3

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step11: Analyze III.4

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step12: Analyze III.5

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step13: Analyze III.6

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step14: Analyze III.7

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step15: Analyze III.8

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step16: Analyze III.9

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step17: Analyze III.10

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step18: Analyze III.11

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Step19: Analyze III.12

The hypotenuse and one leg are marked equal, so it is congruent by HL.

Answer:

II.7: ASA
II.8: ASA
II.9: AAS
II.10: ASA
II.11: ASA
II.12: AAS
III.1: HL
III.2: HL
III.3: HL
III.4: HL
III.5: HL
III.6: HL
III.7: HL
III.8: HL
III.9: HL
III.10: HL
III.11: HL
III.12: HL