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REINFORCE The largest two angles of a triangle are four and five times as large as the triangle's smallest angle, respectively. a. Find the measures of all three of the triangle's angles. b. What special type of triangle is this triangle?

REINFORCE The largest two angles of a triangle are four and five times as large as the triangle's smallest angle, respectively. a. Find the measures of all three of the triangle's angles. b. What special type of triangle is this triangle?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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nq.com/web/viewer.html?source=extension_pdfhandler&extension_handler=extension_open_button&file=https%3A P O 0407_TrianglesProperties_SAS3-student.pdf Properties of a triangle Student Activity Sheet 3; Exploring "Triangle angle theorems" Page 3 of 6 9. REINFORCE The largest two angles of a triangle are four and five times as large as the triangle's smallest angle, respectively. a. Find the measures of all three of the triangle's angles. b. What special type of triangle is this triangle? 10. REINFORCE In the diagram, j || k. Find the values of x and y. 58 42 11. REINFORCE The lengths of three sides of a triangle are 2x, 3x - 4, and x + 4. Find a value of x that makes the triangle equilateral.
Transcribed Image Text:nq.com/web/viewer.html?source=extension_pdfhandler&extension_handler=extension_open_button&file=https%3A P O 0407_TrianglesProperties_SAS3-student.pdf Properties of a triangle Student Activity Sheet 3; Exploring "Triangle angle theorems" Page 3 of 6 9. REINFORCE The largest two angles of a triangle are four and five times as large as the triangle's smallest angle, respectively. a. Find the measures of all three of the triangle's angles. b. What special type of triangle is this triangle? 10. REINFORCE In the diagram, j || k. Find the values of x and y. 58 42 11. REINFORCE The lengths of three sides of a triangle are 2x, 3x - 4, and x + 4. Find a value of x that makes the triangle equilateral.
O 0407_TrianglesProperties_SAS3-student.pdf Properties of a triangle Student Activity Sheet 3; Exploring “Triangle angle theorems" Page 4 of 6 12. What is the name for two angles that have a sum of 90? Two angles are called complementary if their measures add to 90 degrees, 13. Write a conjecture about the acute angles of a right triangle. two acute angles that add up to 90° the three angles of any triangle always add up to 180°. 14. Prove your conjecture from the previous question. Given: AQSR is a right triangle with a right angle at Q. Prove: ZR and 2s are complementary. Statements Reasons 1. mzQ = 90° 1. Given, definition of a right angle 2. mzQ + mZR+ m2 2. Theorem 180° 3. +mzR+ mzS = 180° 3. Substitution Property 4. m<R + m2S = | | 4. Subtraction Property 5. ZR and ZS are complementary. 5. Definition of
Transcribed Image Text:O 0407_TrianglesProperties_SAS3-student.pdf Properties of a triangle Student Activity Sheet 3; Exploring “Triangle angle theorems" Page 4 of 6 12. What is the name for two angles that have a sum of 90? Two angles are called complementary if their measures add to 90 degrees, 13. Write a conjecture about the acute angles of a right triangle. two acute angles that add up to 90° the three angles of any triangle always add up to 180°. 14. Prove your conjecture from the previous question. Given: AQSR is a right triangle with a right angle at Q. Prove: ZR and 2s are complementary. Statements Reasons 1. mzQ = 90° 1. Given, definition of a right angle 2. mzQ + mZR+ m2 2. Theorem 180° 3. +mzR+ mzS = 180° 3. Substitution Property 4. m<R + m2S = | | 4. Subtraction Property 5. ZR and ZS are complementary. 5. Definition of
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