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Bell Work Warm Up Solve each proportion If ∆QRS ~ ∆XYZ, identify the pairs of congruent angles and write 3 proportions using pairs of corresponding sides. z = ±10  Q   X;  R   Y;  S   Z; x = 8

There are 182 girls in the sophomore class of 305 students. What is the ratio of girls to total students? The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet. Find the measure of each side of the triangle. 24 ft, 32ft, 48ft 3. The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is 84 ft. Find the measure of each side of the triangle. 21 in, 27in, 36 in 4. 5 = x 8 12 X = 7.5

Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement. 2. The ratio of a model sailboat’s dimensions to the actual boat’s dimensions is. If the length of the model is 10 inches, what is the length of the actual sailboat in feet? no 25 ft

7.2 Determine if ∆ JLM ~ ∆ NPS. If so, write the similarity ratio and a similarity statement. Step 1 Identify pairs of congruent angles.  N   M,  L   P,  S   J Step 2 Compare corresponding sides. Thus the similarity ratio is, and ∆LMJ ~ ∆PNS.

Explain why the triangles are similar and write a similarity statement. 2. Explain why the triangles are similar, then find BE and CD.

answers 1. By the Isosc. ∆ Thm.,  A   C, so by the def. of , m  C = m  A. Thus m  C = 70° by subst. By the ∆ Sum Thm., m  B = 40°. Apply the Isosc. ∆ Thm. and the ∆ Sum Thm. to ∆PQR. m  R = m  P = 70°. So by the def. of ,  A   P, and  C   R. Therefore ∆ABC ~ ∆PQR by AA ~. 2.  A   A by the Reflex. Prop. of . Since BE || CD,  ABE   ACD by the Corr.  s Post. Therefore ∆ABE ~ ∆ACD by AA ~. BE = 4 and CD = 10.