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PERIOD DATE NAME Practice Proving Angle Relationships Find the measure of each numbered angle and name the theorems that justify your work. l./nZl =x + 10 mZ2 = 3x + 18 2. mZ4 = 2x - 5 mZ5 = 4x - 13 3. mZ6 = Ix - 24 mZ7 = 5* + 14 '/ h. \c 4. Write a two-column proof. Given: Zl and Z2 form a linear pair. Z2 and Z3 are supplementary. Prove: Zl = Z3 o I ± 5. STREETS Refer to the figure. Barton Road and Olive Tree Lane form a right angle at their intersection. Tryon Street forms a 57° angle with Olive Tree Lane. What is the measure of the acute angle Tryon Street forms with Barton Road? Chapter 2 52 Barton Rd Fryon St Olive Tree Lane Glencoe Geometry DATE NAME PERIOD Word Problem Practice Proving Angle Relationships 1. ICOSAHEDRA For a school project, students are making a giant icosahedron, which is a large solid with many identical triangular faces. John is assigned quality control. He must make sure that the measures of all the angles in all the triangles are the same as each other. He does this by using a precut template and comparing the corner angles of every triangle to the template. How does this assure that the angles in all the triangles will be congruent to each other? o I d o 4. PAINTING Students are painting their rectangular classroom ceiling. They want to paint a line that intersects one of the corners as shown in the figure. 15° Cross section of pipe They want the painted line to make a 15° angle with one edge of the ceiling. Unfortunately, between the line and the edge there is a water pipe making it difficult to measure the angle. They decide to measure the angle to the other edge. Given that the corner is a right angle, what is the measure of the other angle? 2. VISTAS If you look straight ahead at a scenic point, you can see a waterfall. If you turn your head 25° to the left, you will see a famous mountain peak. If you turn your head 35° more to the left, you will see another waterfall. If you are looking straight ahead, through how many degrees must you turn your head to the left in order to see the second waterfall? 5. BUILDINGS Clyde looks at a building from point E. Z.AEC has the same measure as /J3ED. Hi TS I I 3. TUBES A tube with a hexagonal cross section is placed on the floor. a. The measure of /.AEC is equal to the sum of the measures of /.AEB and what other angle? O O I _0> o © b. The measure of /.BED is equal to the sum of the measures of /.CED and what other angle? 120V 1 I, What is the measure of Zl in the figure given that the angle at one corner of the hexagon is 120°? Chapter 2 c. Is it true that m/.AEB is equal to 53 Glencoe Geometry Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. O BJ TJ Practice Word Problem Practice Proving Angle Relationships Proving Angle Relationships Find the measure of each numbered angle and name the theorems that justify your work. 1. mZl = * + 10 mZ2 = 3x + 18 mZ1 = 48, mZ2 = 132 Supp. Thm. 2. mZ4 = 2x - 5 mZ5 = 4* - 13 mZ3 = 90, mZ4 = 31, mZ5 = 59 Supp. and Comp, Thm. 3. mZ6 = 7* - 24 mZ7 = 5* -+• 14 mZ6 = 109, mZ7 = 109 Vert. A. Thm. 4. Write a two-column proof. Given: Zl and Z2 form a linear pair. Z2 and Z3 are supplementary. Prove: Zl = Z3 10 cn ,\ VT Proof: Statements Reasons 1. Z1 Z2 2. Z1 3. Z1 1. Given 2. Supplement Theorem 3. A. suppl. to the same Z or s A are =. and Z2 form a linear pair and Z3 are supplementary. and Z2 are supplementary. == Z3 1. ICOSAHEDRA For a school project, students are making a giant icosahedron, which is a large solid with many identical triangular faces. John is assigned quality control. He must make sure that the measures of all the angles in all the triangles are the same as each other. He does this by using a precut template and comparing the corner angles of every triangle to the template. How does this assure that the angles in all the triangles will be congruent to each other? 4. PAINTING Students are painting their rectangular classroom ceiling. They want to paint a line that intersects one of the corners as shown in the figure. Cross section of pipe They want the painted line to make a 15° angle with one edge of the ceiling. Unfortunately, between the line and the edge there is a water pipe making it difficult to measure the angle. They decide to measure the angle to the other edge. Given that the corner is a right angle, what is the measure of the other angle? 75 By the Transitive Property, if any two angles are equal to the angle of the template, then they must be equal to each other. 2. VISTAS If you look straight ahead at a scenic point, you can see a waterfall. If you turn your head 25° to the left, you will see a famous mountain peak. If you turn your head 35° more to the left, you will see another waterfall. If you are looking straight ahead, through how many degrees must you turn your head to the left in order to see the second waterfall? 60 5. BUILDINGS Clyde looks at a building from point E. ZA£C has the same measure as ZBED. CD 10 <D 03 CO O 3 00 3. TUBES A tube with a hexagonal section is placed on the floor. 5. STREETS Refer to the figure. Barton Road and Olive Tree Lane form a right angle at their intersection. Tryon Street forms a 57° angle with Olive Tree Lane. What is the measure of the acute angle Tryon Street forms with Barton Road? 33 a. The measure of ZAEC is equal to the sum of the measures of ZAEB and what other angle? ZBEC b. The measure of ^.BED is equal to the sum of the measures of Z CED and what other angle? ZBEC What is the measure of Z1 in the figure given that the angle at one corner of the hexagon is 120°? 60 c. Is it true that m/.AEB is equal to mZCED? yes 8 CD O CD O Chapter 2 52 CD Answers Glencoe Geometry Chapter 2 53 Glencoe Geometry