1. A(0, 5), B(3, 2), C(6, -1), D(8, -3), E(9, -4)
2. Lengths: AC = √[(10-7)² + (10-7)²] = √18 = 3√2, BC = √[(10-7)² + (10-7)²] = √18 = 3√2, AB = √[(10-10)² + (10-7)²] = 3. For triangle CDE: CD = √[(7-5)² + (7-5)²] = √8 = 2√2, DE = √[(5-5)² + (5-7)²] = 2, CE = √[(7-5)² + (7-5)²] = √8 = 2√2. Ratios: AC/CD = (3√2)/(2√2) = 3/2, BC/CE = (3√2)/(2√2) = 3/2, AB/DE = 3/2. Since all corresponding sides are proportional, triangles ABC and CDE are similar by SSS similarity.
3. Triangle PQR has vertices P(4,4), Q(0,4), R(0,0). Triangle STR has vertices S(-4,0), T(-4,-4), R(0,0). PQ = 4, QR = 4, PR = √[(4-0)² + (4-0)²] = √32 = 4√2. ST = 4, TR = 4, SR = √[(-4-0)² + (0-0)²] = 4. Ratios: PQ/ST = 4/4 = 1, QR/TR = 4/4 = 1, PR/SR = (4√2)/4 = √2. The ratios are not equal, so the triangles are not similar.
4. Calculate slopes between points. Slope between (1,5) and (2.5,9.5): m1 = (9.5-5)/(2.5-1) = 4.5/1.5 = 3. Slope between (2.5,9.5) and (4.5,15.5): m2 = (15.5-9.5)/(4.5-2.5) = 6/2 = 3. Since the slopes are equal, the points lie on the same line.
Parent Tip: Review the logic above to help your child master the concept of similar triangles worksheet 8th grade.
