University:
High School
Course:
High School Geometry
Academic year:

2022
Views:

149

Pages:

12
Author:

Bruno Cain

Contents: Chapter 1 1. a) What point is collinear with D? * Points on the same line * Point E or C b) Name the point of intersection of CD with plane A. * Where they touch at * Point E c) Name a point that is not coplanar with G. * Points Not on the same plane * Points E or C d) Name one pair of opposite rays. * Rays connected and to make a line * GE and EC or EB and ED a) Write four names for the angle. ∠XYZ ∠ZYX ∠Y ∠7 b) Find m∠BAD ∠BAD = 55° c) If m∠PRS = 98°, find m∠QRS ∠PRS = ∠PRQ + ∠QRS 98° = (3x - 8)° + (2x + 6)° 98 = 5x - 2 100 = 5x 20° = x ∠QRS = (2x + 6)° = (2 * 20 + 6)° = 46° d) Find x 180° = (2x - 18)° + (4x)° 180 = 6x - 18 198 = 6x 33 = x e) Find m∠WXZ (7x - 10)° + (2x + 1)° = 90° 9x - 9 = 90° 9x = 99° x = 11° ∠WXZ = (2x + 1)° = (2 * 11 + 1)° = 23° 7. Name the angle(s) that fit the description. a) Linear pair with ∠4 ∠1 and ∠4 ∠3 and ∠4 b) Adjacent to ∠2 Share a side ∠1 or ∠3 c) Vertical to ∠3 Opposite and made across ∠5 d) Complementary to ∠1 Finish the 90° ∠5 1. Find the scale factor. Then list all pairs of congruent angles and write the ratio of the corresponding side lengths in a statement of proportionality. ΔABC ~ ΔHIJ Scale Factor: 1/3 Congruent Angles: ∠A ≅ ∠H, ∠B ≅ ∠I, ∠C ≅ ∠J Proportionality: HI/AB = HJ/AC = IJ/BC 2. Determine whether the triangles are similar. Explain your reasoning. a) Yes, Similar by AA b) Yes, by SSS c) No, only one set of ≅ angles d) Yes, by SAS 3. Find the value of x in the similar polygons. a) x = 22.5 b) x = 9 3. Find the value of x in the similar polygons. c) Diagram: Two similar triangles with side lengths labeled. Solution: 10/x = 4/(x+1) 10(x+1) = 4x 10x + 10 = 4x 6x = -10 x = -5/3 d) Diagram: Two similar triangles with side lengths labeled. Solution: 2x/2x+3 = 9/24 24(2x) = 9(2x+3) 48x = 18x + 27 30x = 27 x = 9/10 e) Diagram: Two triangles with corresponding sides parallel. Solution: 10/x = 7.2/5 10 * 5 = 7.2 * x 50 = 7.2x x = 50/7.2 = 25/3.6 ≈ 6.9 f) Diagram: Two similar triangles with side lengths labeled. Solution: x/36 = 9/20 20x = 9 * 36 20x = 324 x = 16.2 4. Find the Perimeter of ΔLMN in the similar polygons if the perimeter of ΔABC is 9cm * Diagram: Two similar triangles with side lengths labeled. * Solution: * Perimeter Ratio = Side Ratio * 9/x = 6/14 * 6x = 9 * 14 * 6x = 126 * x = 21 * Perimeter of ΔLMN = 21 cm 5. Find the Area of ΔABC in the similar polygons if the area of ΔLMN is 73.5 cm² * Diagram: Two similar triangles with side lengths labeled. * Solution: * Area Ratio = (Side Ratio)² * x/73.5 = (6/14)² * x/73.5 = 9/49 * 49x = 73.5 * 9 * 49x = 661.5 * x = 13.5 cm² * Area of ΔABC = 13.5 cm²