University:
Glendale Community College
Course:
MAT140 | College Mathematics
Academic year:

2022
Views:

347

Pages:

4
Author:

5prinzg1s

THE PYTHAGOREAN THEOREM Part I (20 points) In problems 1-5, simplify each radical completely. 4 a ^ 2 + b ^ 2 sqrt(1/5) In problems 6-10, solve for x. 6 x ^ 2 + 7x - 30 = 0 1 2 3 4 5 6 7 x ^ 2 = 9x 7 8 x ^ 2 + 5 ^ 2 = 13 ^ 2 8 9 x ^ 2 + (3sqrt(2)) ^ 2 = (sqrt(26)) ^ 2 9 10 6x ^ 2 + 18x = 24 10 In problems 11-20, find the length of each segment named with a letter. 11 A = 11 1.3 0.5 9 12 B = underline ? 12 A 41 13 C = underline ? 13 70 14 D = underline -? 10 D 12 14 C 15 E = underline ? 15 16 F = underline ? E 123 15 16 17 G = underline ? 36 17 2√3 246 Class Date THE PYTHAGOREAN THEOREM (continued) 18 H ? H 191? 20 J? Part II (22 points) 21 If BC 4 and AB 8, find CD. 6 C 18 16 19 J 20 21 A B D 22 M is the midpoint of a side of rectangle P M Q PQRS. Find the perimeter. T T of AMST. 7 22 S R 24 23 Classify a triangle with sides of lengths 8, 11, and 14 as acute, right, or obtuse. 24 A succession of squares is formed by joining the midpoints of each square. ABCD is 8, find the square. If each side of the square perimeter of the shaded A 23 24 C 25 Find x. 12 135 30" 25 THE PYTHAGOREAN THEOREM (continued) 26 Find the length of a diagonal of the cube, each of whose sides is 10. 27 Find BC. (LC is not a right L.) 26 10 C 27 A 28 The slant height of the regular square pyramid shown is 26 and the altitude of the pyramid is 24. Find the length of the diagonal of the base of the pyramid. 3√3 B 29 The distance from chord AB to the center of O is the length of the segment from O to M, the midpoint of AB. How far is AB from O? 28 y (2,2 A в (6,4) 0 6,-1) 29 30 Find the perimeter of the isosceles trapezoid shown. 15 10 30 THE PYTHAGOREAN THEOREM (continued) 31 Given: PQRT is a square. P Q ABCS is a square. AAPS is equilateral Find RS, correct to the nearest tenth. A R T 31 B C 10 Part III (8 points) In problem 32, draw a diagram on the axes and coordinatize the diagram appropriately. Write the given and conclusion in terms of the diagram. Then write an analytic proof. 32 The length of the median to the hypotenuse of a right triangle is half the length of the hypotenuse. y