Question

Based only on the information given in the diagram, it is guaranteed that ABC DEF.

Answer 1

Answer:

B) False

Step-by-step explanation:

The information given in the diagram is the measure of two angles of each triangle.

We see that ∠B ≅ E and ∠A ≅ ∠E.  Since we have two angles in both triangles congruent, by the AA postulate this says that the third angle in both triangles must be congruent as well.

Two triangles whose angle measures are the same are similar.  However, they are not guaranteed to be congruent because they are similar; this is false.

Answer 2

Answer: A.True

Step-by-step explanation:

In the given picture we can see that ∠B ≅ E=31° and ∠A ≅ ∠D=90°[right angle].  As we have two angles in both triangles are congruent.

So by AA similarity postulate, we have

ΔABC≈ΔDEF

Thus, based  only on the information given in the diagram, it is guaranteed that ΔABC≈ΔDEF.

AA Similarity Postulate tells that two triangles are similar if they have two corresponding angles that are congruent or equal in measure.