Answer:
∠E and ∠A are right angles; therefore, these angles are congruent since all right angles are congruent. 12 over 4 equals 9 over 3 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SAS Similarity Postulate.
Step-by-step explanation:
Well, I know its not 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 SSS Similarity Postulate," because I took the test. Also, C makes no sense because its talking about angles in the description but then it says that its congruent by sss. And I don't think that it is A. either because it is again talking about how side angles are similar, but then states that its congruent by sas. Honestly, I thinks it that one.
**oh wait I realize that thats not an answer choice for you , ooops**
Similar triangles may or may not be congruent triangles.
The true statement is (d) ∠DCE is congruent to ∠CBA by the Vertical Angles Theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SSS Similarity Postulate.
From the figure, we have the following corresponding sides:
The means that, the following equivalent ratio (k) is true
[tex]\mathbf{k =\frac{DE}{AB} = \frac{CE}{AC} = \frac{DC}{BC}}[/tex]
So, we have:
[tex]\mathbf{k =\frac{9}{3} = \frac{12}{4} = \frac{15}{5}}[/tex]
The above gives
[tex]\mathbf{k =3}[/tex]
This means that, the triangles are similar by SSS postulate (all three sides are corresponding).
And ∠DCE and ∠CBA are congruent by vertical angles theorem.
Hence, the true statement is: (d)
Read more about similar triangles at:
https://brainly.com/question/14926756
