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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

Based only on the information given in the diagram which congruence theorems or postulates could be given as reasons why ABCDEF Check all that apply A HA B HL C class=

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JeanaShupp

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.

boffeemadrid

Answer:

Step-by-step 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.

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