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Prove that ΔABC and ΔEDC are similar.

A. 15 over 4 equals 12 over 5 equals 9 over 3 shows the corresponding sides are proportional; therefore, ΔABC ~ ΔEDC by the SAS Similarity Postulate.

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.

C. ∠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 SSS Similarity Postulate.

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.

Prove That ΔABC And ΔEDC Are Similar A 15 Over 4 Equals 12 Over 5 Equals 9 Over 3 Shows The Corresponding Sides Are Proportional Therefore ΔABC ΔEDC By The SAS class=

Sagot :

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**

MrRoyal

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:

  • AB and DE
  • AC and CE
  • BC and DC

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

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