Expert answers to "Based on the drawing below, in order for..."

High School
Geometry
High school geometry
Similarity

Tabansi

Answered question

2021-08-11

Based on the drawing below, in order for

△ A B C

to be similar to

△ D E F

by SAS similarity, which of the following needs to be true?

m ∠ D = 38^{\circ}

m ∠ D = 52^{\circ}

m ∠ F = 38^{\circ}

m ∠ F = 52^{\circ}

Answer & Explanation

aprovard

Skilled2021-08-12Added 94 answers

Step 1
Angle C needs to be equal to angle F for these triangles to be similar by SSS.
Step 2
For SAS similarity we need two sides and the angle between them.
We see that

\frac{B C}{A C} = \frac{E F}{F D} = \frac{4}{5}

Hence the

∠ B C A = ∠ E F D \Rightarrow ∠ C = ∠ F

(The angle BC and AC. and the angle between EF and FD)

\Rightarrow ∠ F = ∠ C = 38^{\circ}

\Rightarrow m ∠ F = 38^{\circ}

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