Question

B
8
12
E
52 deg
38 deg
A
10
C
F
15
D
What must be true about the angles in triangle DE F dagger it to be similar to triangle ABC by SAS similarity?
A m angle D = 38 deg

Answer 1

I’m missing how the triangles are labeled — which side lengths belong to which vertices and which angles are at which vertices. Can you confirm the triangle data (for example: AB = ?, BC = ?, AC = ?, and DE = ?, EF = ?, DF = ?, and which angles are 52° and 38°)? A picture or a clear list like “In triangle ABC: AB = 8, BC = 12, ∠B = 52° …” will let me answer whether m∠D = 38° is required.

Quick note on SAS similarity you can use once you give the labels:
- Two triangles are similar by SAS if two pairs of corresponding sides are in the same ratio AND the included angles between those sides are equal.
- So the angle in triangle DEF that must equal a given angle in triangle ABC is the included angle between the two sides you are matching. If the angle you propose (∠D) is the included angle between the two matching sides, then it must equal the corresponding angle in ABC; otherwise it does not have to equal 38°.