Question

for questions 3 & 4. Determine whether the triangles are similar. If similar, state how (SA, SSS, or SAS), and write a similarity statement

Answer 1

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Answer:

3. ΔBEA ~ ΔBCD by AA

4. ΔPXY ~ ΔPQR by SSS

Explanation:

3. The missing angle in ΔBEA is angle E, which has measure ...

∠E = 180° -42° -53° = 85°

So, angle E matches angle C, and the vertical angles match. The two triangles are similar by AA. The corresponding angles are B:B, and E:C, so the similarity statement needs to reflect that: ΔBEA ~ ΔBCD.

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4. Shortest-to-longest, the side ratios of the two triangles are ...

12 : 15 : 18 = 4 : 5 : 6

and

16 : 20 : 24 = 4 : 5 : 6

Side ratios are proportional, so the triangles are similar by SSS. The similarity statement can reflect the same ordering: ΔPXY ~ ΔPQR.