HPT13 Properties of Triangles and our-sided igures Lesson 13.1 lassifying Triangles 1. lassify the following triangles by sides as a scalene triangle, an isosceles triangle, or an equilateral triangle. G H L P K X M N S K Y Z Marshall avendish International (Singapore) Private Limited. T U Scalene Triangles quilateral Triangles Isosceles Triangles xtra Practice 5 101
2. lassify the following triangles by angles as a right triangle, an isosceles triangle, or an equilateral triangle. Use a protractor to help you classify the triangles. G H K L P S M N V X T U W X Y Z ight Triangles quilateral Triangles Isosceles Triangles Marshall avendish International (Singapore) Private Limited. 102 hapter 13 Lesson 13.1
Lesson 13.2 Measures of ngles of a Triangle ind the unknown angle measures. The figures are not drawn to scale. 1. 38 a 46 m a 2. 39 115 e m e 3. Marshall avendish International (Singapore) Private Limited. 4. g 28 G 45 19 H m g m f 76 f xtra Practice 5 103
5. T t 88 30 V m t U 6. 35 36 r S m r T 7. X V 28 53 W y Y m y 8. 29 37 a 47 m a Marshall avendish International (Singapore) Private Limited. 104 hapter 13 Lesson 13.2
Lesson 13.3 ight, Isosceles, and quilateral Triangles ind the unknown angle measures in each right triangle. The figures are not drawn to scale. 1. is a right triangle. ind the measure of. 58 2. P is a right triangle. ind the measure of P. Marshall avendish International (Singapore) Private Limited. P 37 xtra Practice 5 105
ind the unknown angle measures. The figures are not drawn to scale. 3. is a right triangle. ind the measure of. 36 47 4. is an isosceles triangle with, m 34, and m 44. ind the measure of. 44 34 Marshall avendish International (Singapore) Private Limited. 106 hapter 13 Lesson 13.3
ind the unknown angle measures in each figure. The figures are not drawn to scale. 5. O is an isosceles triangle. O O. O is a right triangle. ind the measure of O 24 O 6. is an equilateral triangle and is an isosceles triangle. ind the measure of. Marshall avendish International (Singapore) Private Limited. xtra Practice 5 107
7. is a 6-sided figure. ll the triangles are equilateral triangles. ind the measure of. 8. is an equilateral triangle.. ind the measure of. 28 Marshall avendish International (Singapore) Private Limited. 108 hapter 13 Lesson 13.3
Lesson 13.4 Triangle Inequalities omplete. Measure the sides of the triangle to the nearest inch. P 1. P in. in. P in. 2. P in. 3. P P in. 4. P in. Marshall avendish International (Singapore) Private Limited. Use your answers in xercises 1 to 4. ill in the blanks with Yes or No. 5. Is P P? 6. Is P P? 7. Is P P? xtra Practice 5 109
omplete. Measure the sides of the triangle to the nearest centimeter. 8. cm cm cm 9. cm 10. cm 11. cm Use your answers in xercises 8 to 11. Write the sides of the triangle to make the inequalities true. 12. 13. 14. Marshall avendish International (Singapore) Private Limited. 110 hapter 13 Lesson 13.4
The lengths of two sides of each triangle are given. Name a possible length for the third side. The given lengths are in whole centimeters or inches. 15. Z 2 in.? X 4 in. Y In triangle XYZ, the length of ZY is greater than 2 inches. possible length of ZY, rounded to the nearest inch, is. 16. G? 5 cm Marshall avendish International (Singapore) Private Limited. 4 cm In triangle G, the length of G is greater than 4 centimeters. possible length of G, rounded to the nearest centimeter, is. xtra Practice 5 111
The lengths of two sides of each triangle are given. Name a possible length for the third side. The given lengths are in whole centimeters or whole inches. 17. U 9 cm? S 8 cm T In triangle STU, the length of UT is less than 10 centimeters. possible length of UT, rounded to the nearest centimeter, is. 18. 2 in.? P 3 in. In triangle P, the length of is greater than 3 inches. The possible length of, rounded to the nearest inch, is. Marshall avendish International (Singapore) Private Limited. 112 hapter 13 Lesson 13.4
Lesson 13.5 Parallelogram, hombus, and Trapezoid ind the unknown angle measures. The figures are not drawn to scale. 1. G is a parallelogram and G GH. ind the measure of y. H 48 64 y G 2. PS is a parallelogram and ST is a right triangle. ind the measures of PS and ST. Marshall avendish International (Singapore) Private Limited. 118 P S T xtra Practice 5 113
3. and are parallelograms. ind the measure of. 108 59 4. PS is a rhombus and P T. ind the measure of P. P S T 116 Marshall avendish International (Singapore) Private Limited. 114 hapter 13 Lesson 13.5
5. WXYZ is a rhombus and WV is a line segment. ind the measure of VYZ. X W 128 Y V Z 6. is a rhombus. is a line segment. ind the measure of x. 108 64 Marshall avendish International (Singapore) Private Limited. x xtra Practice 5 115
7. PS is trapezoid and S P. S P. ind the measure of P. S 67 P 58 8. is a trapezoid. and. is a line. ind the measure of. 130 96 Marshall avendish International (Singapore) Private Limited. 116 hapter 13 Lesson 13.5
Put on Your Thinking ap! The figures are not drawn to scale. ind the unknown angle measures. 1. PS and STUV are parallelograms and PT PU. ind the measure of SV. U 118 V P T S 2. PS is a parallelogram and ST SP. ind the measure of a. Marshall avendish International (Singapore) Private Limited. T S 106 P a xtra Practice 5 117
3. is a square and is a rhombus. ind the measure of. 54 4. G is a trapezoid and G. and are isosceles triangles. ind the measures of x and y. 32 y G x Marshall avendish International (Singapore) Private Limited. 118 hapter 13 Put on Your Thinking ap!
5. In the figure, PS P and the measure of STP is twice the measure of TPS. ind the measures of x and y. y T S P x 27 6. is an equilateral triangle. is an isosceles triangle, where, m 54, and m 118. ind the measures of x and y. Marshall avendish International (Singapore) Private Limited. x 118 54 y G xtra Practice 5 119
7. is a rectangle. and G. ind the measures of x and y. G y 34 x 58 8. is a right triangle, G is a line segment, and m m. m 90 and. ind the measures of x and y. G 103 x y 56 Marshall avendish International (Singapore) Private Limited. 120 hapter 13 Put on Your Thinking ap!