Question

Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why ABC~DEF? Check all that apply.

A. HA
B. HL
C. SAS
D. LA
E. AAS
F. SSS

Answer 1

Explanation:

1. HA cannot be a reason to show ABC~DEF as it is not given that they have an acute angle common in both the triangles.

2. HL can be a reason to show given triangles are similar as the triangles are right triangle with equal legs and hypotenuse.

3. SAS can be a reason to show given triangles are similar as

AB=DE(given)

∠A=∠D(90°)

AC=DF(given)

By SAS rule, ΔABC≅DEF.

4. LA cannot be a reason to show given triangles are similar as it is not given that they have an acute angle common in both the triangles.

5. AAS cannot be a reason to show given triangles are congruent as it is not given that they have two angles common in both the triangles.

6.SSS can be a reason to show given triangles are similar as:

AB=DE(given)

AC=DF(given)

BC=EF(given)

By SSS rule,

ΔABC≅DEF.

Answer 2

Answer:- B , C and F are the right options.

Explanation:-

1. HA cannot be a reason to show given triangles are congruent as it is not given that they have an acute angle common in both the triangles.

2. HL can be a reason to show given triangles are congruent as the triangles are right triangle with equal legs and hypotenuse.

3. SAS can be a reason to show given triangles are congruent as there are two congruent sides in both triangles and included angles ∠A=∠D=90° [right angle].

4. LA cannot be a reason to show given triangles are congruent as it is not given that they have an acute angle common in both the triangles.

5. AAS cannot be a reason to show given triangles are congruent as it is not given that they have two angles common in both the triangles.

6.SSS can be a reason to show given triangles are congruent as it is shown that all the sides of one triangle is congruent to the other.