Prove that ΔABC and ΔEDC are similar. triangles ABC and DEC where angles A and E are right angles, AC equals 4, AB equals 3, BC equals 5, DC equals 15, DE equals 9, and CE equals 12

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.

∠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.

∠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.

∠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.

Since shows two corresponding sides are proportional and based on the vertical angles theorem, therefore, we can prove that by the SAS Similarity Theorem. (Option B).

Recall:

In the diagram given,

We know that, based on the vertical angle theorem, <DCE and <BCA are congruent.

If we the two sides that the congruent angles lie in between are proportional, then we can prove that both triangles are congruent by the SAS similar theorem.

Thus:

(this shows proportionality)

Therefore, since shows two corresponding sides are proportional and based on the vertical angles theorem, therefore, we can prove that by the SAS Similarity Theorem. (Option B).

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d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

the answer is 11.2 (i know i’m late)