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

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  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.

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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.

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

chad should not have included the values (1, 2) and (3, 6) because that would mean he only had half a healing card.