Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning.

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1 ARCHITECTURE Classify each triangle as acute, equiangular, obtuse, or right. 1. Refer to the figure on page 240. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a right angle, it is a right triangle. 3. Refer to the figure on page 240. Since all the angles are congruent, the triangle is equiangular. Classify each triangle as acute, equiangular, obtuse, or right. Explain your reasoning. 5. In,. So, is obtuse. Since the triangle has an obtuse angle, it is obtuse. CCSS PRECISION Classify each triangle as equilateral, isosceles, or scalene. 7. The triangle has two congruent sides. So, it is isosceles. esolutions Manual - Powered by Cognero Page 1

2 If point K is the midpoint of, classify each triangle in the figure as equilateral, isosceles, or scalene. 9. In, K is the midpoint of. So,. So, all the sides of have equal lengths. Therefore, is equilateral. 11. In, K is the midpoint of. So,. Also, HL = 3 and FL = 7. No two sides are congruent in. Therefore, it is scalene. esolutions Manual - Powered by Cognero Page 2

3 ALGEBRA Find x and the measures of the unknown sides of each triangle. 13. In the figure, So any combination of two side measures can be used to find x. Substitute in QR.. Since all the sides are congruent, QR = RS = QS = 25. Classify each triangle as acute, equiangular, obtuse, or right. 15. One angle of the triangle measures 115, so it is a obtuse angle. Since the triangle has an obtuse angle, it is an obtuse triangle. 17. One angle of the triangle measures 90, so it is a right angle. Since the triangle has a right angle, it is a right triangle. 19. The triangle has three acute angles. It is an acute triangle. esolutions Manual - Powered by Cognero Page 3

4 CCSS PRECISION Classify each triangle as acute, equiangular, obtuse, or right. 21. In,. So, is obtuse. Since the triangle has an obtuse angle, it is obtuse. 23. All the angles are acute angles in. So, it is an acute triangle. 25. In,. So, is a right angle. Since the triangle has a right angle, it is a right triangle. Classify each triangle as equilateral, isosceles, or scalene. 27. Refer to the figure on page 241. Since all the sides are congruent, the triangle is equilateral. esolutions Manual - Powered by Cognero Page 4

5 29. Refer to the figure on page 241. No two sides are congruent in the given triangle, so it is scalene. If point C is the midpoint of and point E is the midpoint of, classify each triangle as equilateral, isosceles, or scalene. 31. Here, E is the midpoint of. So, DE = EF = 5. In, all the sides are having different lengths. So, it is scalene. 33. No two sides are congruent in. So, it is scalene. 35. Here, C is the midpoint of. So, BC = CD = 4. Also by Segment Addition Postulate, BC = BC + CD = 8. In, AB = 8, BD = 8, and AD = 8. All the sides are congruent in. So, it is equilateral. esolutions Manual - Powered by Cognero Page 5

6 37. ALGEBRA Find x and the length of each side if is an equilateral triangle. Since is an equilateral triangle, So any combination of sides can be used to find x. Let's use Solve for x. Substitute in FG. Since all the sides are congruent, FG = GH = HF = KALEIDOSCOPE Josh is building a kaleidoscope using PVC pipe, cardboard, bits of colored paper, and a 12-inch square mirror tile. The mirror tile is to be cut into strips and arranged to form an open prism with a base like that of an equilateral triangle. Make a sketch of the prism, giving its dimensions. Explain your reasoning. Because the base of the prism formed is an equilateral triangle, the mirror tile must be cut into three strips of congruent width. Since the original tile is a 12-inch square, each strip will be 12 inches long by 12 3 or 4 inches wide. esolutions Manual - Powered by Cognero Page 6

7 CCSS PRECISION Classify each triangle in the figure by its angles and sides. 41. In the figure,. has two congruent sides and an obtuse angle. So, it is an isosceles obtuse triangle. COORDINATE GEOMETRY Find the measures of the sides of sides. 43. X( 5, 9), Y(2, 1), Z( 8, 3) Graph the points on a coordinate plane. and classify each triangle by its Use the Distance Formula to find the lengths of. has endpoints X( 5, 9) and Y(2, 1). has endpoints Y(2, 1) and Z( 8, 3). esolutions Manual - Powered by Cognero Page 7

8 has endpoints X( 5, 9) and Z( 8, 3). No two sides are congruent. So, it is scalene. esolutions Manual - Powered by Cognero Page 8

9 45. X(3, 2), Y(1, 4), Z(3, 4) Graph the points on a coordinate plane. Use the Distance Formula to find the lengths of. has end points X(3, 2) and Y(1, 4). has endpoints Y(1, 4) and Z(3, 4). has endpoints X(3, 2) and Z(3, 4). YZ = XZ = 2. This triangle has two congruent sides. So, it is isosceles. esolutions Manual - Powered by Cognero Page 9

10 47. PROOF Write a paragraph proof to prove that is an acute triangle if and is acute. Given: Prove: is acute. Proof: and form a linear pair. and are supplementary because if two angles form a linear pair, then they are supplementary. So,. We know, so by substitution,. Subtract to find that. We already know that is acute because is acute. must also be acute because is acute and. is acute by definition. ALGEBRA For each triangle, find x and the measure of each side. 49. is an equilateral triangle with FG = 3x 10, GH = 2x + 5, and HF = x Since is equilateral, FG = GH = HF. Consider FG = GH. 3x 10 = 2x + 5 3x 10 2x = 2x + 5 2x x 10 = 5 x =15 Substitute x =15. Since all the sides are congruent, FG = GH = HF = 35. esolutions Manual - Powered by Cognero Page 10

11 51. is isosceles with. MN is two less than five times x, NP is seven more than two times x, and PM is two more than three times x. Here,. By the definition of congruence,. MN = 5x 2, NP = 2x + 7, PM = 3x + 2 Substitute in MN, NP, and PM. esolutions Manual - Powered by Cognero Page 11

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