Question

(03.05 MC)

Answer 1

Answer:

Option B) ∠DCE is congruent to ∠BCA by the Vertical Angles Theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SAS Similarity Postulate

Step-by-step explanation:

we know that

The SAS Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar

we have that

m∠DCE≅m∠BCA -----> by vertical angles

$\frac{DC}{BC}=\frac{EC}{AC}$

substitute the values

$\frac{15}{5}=\frac{12}{4}$

$3=3$ ----> is true

so

Two sides in triangle ABC are are proportional to two sides in triangle EDC and the included angle in both triangles are congruent

therefore

ΔABC and ΔEDC are similar by  SAS Similarity Postulate