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

9514 1404 393

  3. ΔBEA ~ ΔBCD by AA

  4. ΔPXY ~ ΔPQR by SSS

Step-by-step 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.

__

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.