Triangle LMN and triangle OPN are similar triangles. Find the angle measurements for x, y, and z.
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1 1 Use measurements of the two triangles elow to find x and y. Are the triangles similar or ongruent? Explain. 1a Triangle LMN and triangle OPN are similar triangles. Find the angle measurements for x, y, and z. E x y M x y N 50 z O R 4 38 L D U L 53 P The sum of the measures of angles in a triangle is 180. Therefore to find the missing angle measurements, add up the given measurements and sutrat this numer from Selet all of the following that desrie the triangles shown elow. x = 180 x = 180 x = x = y = 180 y = 180 y = y = 4 The triangles are similar eause they have the same angle measurements. However, we annot onlude that the triangles are ongruent eause we do not know their side lengths. 60 A) oth triangles are similar. ) oth triangles are ongruent. C) The triangles are ongruent ut not similar. D) The triangles are similar ut not ongruent. E) The triangles are neither similar nor ongruent. Page 1 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
2 2 Christopher wants to give his friend a aseall at as a gift for his irthday. He finds a ox that is 16 inhes wide, 30 inhes long, and 12 inhes tall to wrap it in. If the at is 33 inhes long, will it fit in the ox? If the at is 36 inhes long will fit in the ox? Explain. 2a A 25-foot ladder is plaed against a uilding. The ottom of the ladder is feet from the uilding. If the top of the ladder slips down 4 feet, how many feet will the ottom slide out? 30 in. 12 in. in. 16 in. Sine the at is longer than the ox, it will have to fit in the ox at an angle. We an use the Pythagorean Theorem, a = 2, to find the length of the hypotenuse and ompare it with the length of the at. 8.G. 30 in. 16 in. 2 In this figure A and CD are perpendiular. Selet all of the following statements that are true. Justify your answers = = = 2 34 = Sine the hypotenuse is 34 inhes long, the at will fit in the ox. To find out if a 36-inh long at will fit in the ox, we have to ompare it to the diagonal from the top of the ox to the ottom of the ox. A 12 D 14 C 15 d 34 in. 12 in. in. A) The length of AD is 5 units. ) The perimeter of CD is 3 units = d = d = d 2 The at is 36 inhes, and 36 2 = 1296, whih is less than Therefore a 36-inh at an fit in the ox. 8.G. C) The length of AC is 11 units. D) The perimeter of AC is 42 units. 8.G. Page 2 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
3 3 What is the length of line segment PQ shown elow? 3a What is the length of line segment A shown elow? A (-6, 5) (3, -) We an use this segment and draw a right triangle. With the segment as the hypotenuse, we an use the Pythagorean Theorem a = 2 to find its length. 3 8.G.8 Given the points graphed elow. Selet all of the statements that are true. D (2, 9) 6 units E (5, 5) 8 units F (2, 1) Counting the grid lines will give us the length of the legs of the right triangle. 2 = = =100 = ±10 PQ =10 units 8.G.8 A) The distane etween D and E is 4 units. ) The distane etween E and F is 5 units. C) The distane etween D and F is 8 units. D) If the three points were onneted in order, the resulting figure would e a right triangle. 8.G.8 Page 3 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
4 4 Determine whether the triangle shown elow is a right triangle. 4a Determine whether the triangle with side lengths 9 m., 40 m., and 41 m., is a right triangle If the lengths of the sides of a triangle satisfy the Pythagorean equation, a = 2, then the triangle is a right triangle. Sustitute the values into the equation and hek if the equation is true. a = = = = 56 False Sine the equation is False, the triangle is not a right triangle. 4 8.G.6 Selet all of the statements that are true aout the desried triangles. A) A triangle with side lengths 8 m., 15 m, and 1 m., is a right triangle. ) A triangle with side lengths 10 in., 20 in., and 24 in., is a right triangle. C) A triangle with side lengths 9 ft., 12 ft., and 18 ft., is a right triangle. D) A triangle with side lengths 12 m., 16 m., and 20 m., is a right triangle. 8.G.6 8.G.6 Page 4 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
5 5 On the oordinate grid elow, perform the following series of transformations to the preimage, and then state whether the resulting images are ongruent or similar. 5 On the oordinate grid elow, perform the following series of transformations to the preimage, and then state whether the resulting images are ongruent or similar. 1) Translate ΔAC 6 units right and 1 unit down and lael the points A!,!, and C!. 1) Reflet ΔDEF aout the x-axis and lael the points D!, E!, and F!. 2) Reflet Δ A " " C " aout the x-axis and lael the points A!!,!!, and C!!. 2) Rotate Δ D " E " F" 90 lokwise aout the origin and lael the points D!!, E!!, and F!!. A C E D F A A!! C!! C! C!! 8.G.2 A!! Preimages that are translated or refleted remain ongruent to the resulting images; therefore the resulting images aove are ongruent. 8.G.2 Page 5 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
6 6 If the figure elow were refleted aout the y-axis, what would e the oordinates of the verties of the resulting figure? 6a If the figure elow were rotated 180 the to the right aout the origin, what would e the oordinates of C!? (-, -2) S (-1, -2) T R (-4, -6) The refleted figure with its verties is shown elow. (1, -2) T! R! (4, -6) (, -2) S! 6 8.G.3 Selet all of the expressions that desrie the translation from ( 3, 4) to (4, 1). A) units left and 5 units up Notie that the x-oordinate of eah vertex is the opposite, while the y-oordinate remained unhanged. ) units right and 5 units up C) units left and 5 units down D) units right and 5 units down 8.G.3 8.G.3 Page 6 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
7 Parallel lines r and s are interseted y a transversal t. List eah pair of orresponding, alternate interior, and alternate exterior angles. If m 2 is 3, what are the measures of angles 3 and 6? a Parallel lines m and n are interseted y a transversal l. Find the measures of angels a and. m n t r 105 a l s Corresponding angles: 1& 5, 2 & 6, 3&, 4& 8 Alternate Interior angles: 3& 6, 4& 5 Alternate Exterior angles: 1& 8, 2& If m 2 is 3, then m 3 = 3 and m 6 = 3 eause orresponding angles are ongruent and alternate interior angles are ongruent. m Parallel lines m and n are interseted y a transversal t. Selet all of the statements elow that are true. n t A) 2 and 8 are alternate interior angles, therefore they are ongruent. ) 1 and 6 are orresponding angles, therefore they are ongruent. C) m 3, m 5, and m are all equal to m 1. D) 4 and are alternate exterior angles, therefore they are ongruent. Page of 13 MCC@WCCUSD (WCCUSD) 02/23/15
8 8 List eah pair of supplementary and vertial angles. If m 8 = 50 and m 9 =115, find the measures of angles 2, 3, 6, and 10. 8a In the figure elow, line r is parallel to line s. Find the measures of angles a,, and. s t r a s r Supplementary angles: 1& 4, 1& 2, 2 & 3, 3 & 4, 5& 8, 5& 6, 6 &, & 8, 9 & 10, 9 & 12, 10 & 11, 11 & 12 8 In the figure elow, lines g and h are parallel. Selet all of the statements that are true. g 132 a Vertial angles: 1& 3, 2 & 4, 5&, 6 & 8, 9 & 11, 10 & 12 If m 8 = 50 then m 6 = 50 eause vertial angles are ongruent. h A) m d =100. j d 100 e f k If m 9 =115 then m 10 = , or 65 eause angles 9 and 10 are supplementary angles that add to 180. m = 180 eause the sum of the angles in a triangle = 180. Therefore m 3= 65. ) Angles and are supplementary angles. C) Angles d and e are supplementary angles. D) Angles a and are ongruent eause they are vertial angles. Sine m 3= 65, then m 2 = , or 115 eause angles 2 and 3 are supplementary angles that add to 180. E) m a = 48. End of Study Guide Page 8 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
9 You Try Solutions: 1 Selet all of the following that desrie the triangles shown elow. 1a Triangle LMN and triangle OPN are similar triangles. Find the angle measurements for x, y, and z. 30 M x y N 50 z O L L is similar to O therefore z = 53. P A) oth triangles are similar. ) oth triangles are ongruent. C) The triangles are ongruent ut not similar. y = 50 eause similar angles are ongruent. The sum of the measures of angles in a triangle is 180. Therefore to find the missing angle measurements, add up the given measurements and sutrat this numer from 180. D) The triangles are similar ut not ongruent. E) The triangles are neither similar nor ongruent. x = 180 x = 180 x = x = Page 9 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
10 2a A 25-foot ladder is plaed against a uilding. The ottom of the ladder is feet from the uilding. If the top of the ladder slips down 4 feet, how many feet will the ottom slide out? 2 In this figure A and CD are perpendiular. Selet all of the following statements that are true. Justify your answers. A D Use the Pythagorean Theorem to find the height against the uilding efore the ladder slipped down ft. h C 15 A) The length of AD is 5 units. ft = h = h 2 56 = h 2 24 = h ) The perimeter of CD is 3 units. C) The length of AC is 11 units. D) The perimeter of AC is 42 units. The ladder starts out at 24 ft. After it slips, its height is now 24 ft. 4 ft., or 20 ft. high on the uilding. Use this new height with the Pythagorean Theorem to find out how far the ladder is from the uilding. 3a What is the length of line segment A shown elow? 8.G. A (-6, 5) 25 ft. 20 ft = = = 2 15 = 12 units 9 units (3, -) The ladder is now 15 ft. from the uilding, so it slid out 15ft. ft., or 8 ft. 8.G. Use the Pythagorean Theorem to solve for. 2 = = = 225 = 15 units 8.G.8 Page 10 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
11 3 Given the points graphed elow. Selet all of the statements that are true. 4 Selet all of the statements that are true aout the desried triangles. D (2, 9) E (5, 5) A) A triangle with side lengths 8 m., 15 m, and 1 m., is a right triangle. F (2, 1) ) A triangle with side lengths 10 in., 20 in., and 24 in., is a right triangle. C) A triangle with side lengths 9 ft., 12 ft., and 18 ft., is a right triangle. D) A triangle with side lengths 12 m., 16 m., and 20 m., is a right triangle. A) The distane etween D and E is 4 units. 8.G.6 ) The distane etween E and F is 5 units. C) The distane etween D and F is 8 units. D) If the three points were onneted in order, the resulting figure would e a right triangle. 8.G.8 4a Determine whether the triangle with side lengths 9 m., 40 m., and 41 m., is a right triangle. Sustitute the values into the Pythagorean equation and hek if the equation is true. The longest side of a right triangle is the hypotenuse, so = 41 m. a = = = = 1681 True Sine the equation is true, the triangle is a right triangle. 8.G.6 Page 11 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
12 5 On the oordinate grid elow, perform the following series of transformations to the preimage, and then state whether the resulting images are ongruent or similar. 6a If the figure elow were rotated 180 the to the right aout the origin, what would e the oordinates of C!? 1) Reflet ΔDEF aout the x-axis and lael the points D!, E!, and F!. 2) Rotate Δ D " E " F" 90 lokwise aout the origin and lael the points D!!, E!!, and F!!. C! D!!! D! F E! E E!! F!! The oordinates of C! are ( 1, 1). D F Preimages that are refleted or rotated remain ongruent to the resulting images; therefore, the resulting images aove are similar and ongruent. 6 8.G.3 Selet all of the expressions that desrie the translation from ( 3, 4) to (4, 1). 8.G.2 A) units left and 5 units up ) units right and 5 units up C) units left and 5 units down D) units right and 5 units down 8.G.3 Page 12 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
13 a Parallel lines m and n are interseted y a transversal l. Find the measures of angels a and. 8a In the figure elow, line r is parallel to line s. Find the measures of angles a,, and. m n r a a l s m =105 eause alternate exterior angles are ongruent. m a =105 eause a orresponds with and orresponding angles are ongruent. m Parallel lines m and n are interseted y a transversal t. Selet all of the statements elow that are true. n t m a = = 126, eause supplementary angles add to 180. m = 66, eause vertial angles are ongruent. m = 60. It is ongruent (vertial) to the angle in the triangle that when added to 54 and 66 has the sum of 180, sine the angles in a triangle add to In the figure elow, lines g and h are parallel. Selet all of the statements that are true. g h 132 a d 100 e f j k A) 2 and 8 are alternate interior angles, therefore they are ongruent. ) 1 and 6 are orresponding angles, therefore they are ongruent. C) m 3, m 5, and m are all equal to m 1. D) 4 and are alternate exterior angles, therefore they are ongruent. A) m d =100. ) Angles and are supplementary angles. C) Angles d and e are supplementary angles. D) Angles a and are ongruent eause they are vertial angles. E) m a = 48. Page 13 of 13 MCC@WCCUSD (WCCUSD) 02/23/15
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