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1 Natasha uses the Pythagorean Theorem to solve for the length of side b in a right triangle. If the lengths of sides a, b, and c are Pythagorean triples and a and c are odd numbers, what can be assumed about b? A It is an odd number. B It is an even number. C It is a negative number. D No assumption can be made. 2 Which of the following sets of numbers is NOT a Pythagorean triple? F 3, 4, 5 G 8, 15, 17 H 11, 60, 61 J 20, 21, 27 3 A 30-60-90 triangle’s shortest side has a measurement of x. What is the measurement of the other side that includes _ the right angle? A x √2 B 30x C 2x _ D x √3
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solve meaningful problems, including special right tr 7  triangles whose sides are Pythagorean triples. Read each question and choose the best answer. 1 Natasha uses the Pythagorean Theorem to solve for the length of side b in a right triangle. If the lengths of sides a, b, and c are Pythagorean triples and a and c are odd numbers, what can be assumed about b? A It is an odd number. B It is an even number. C It is a negative number. D No assumption can be made. 2 Which of the following sets of numbers is NOT a Pythagorean triple? F 3, 4, 5 G 8, 15, 17 H 11, 60, 61 J 20, 21, 27 3 A 30-60-90 triangle’s shortest side
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3 A 30-60-90 triangle’s shortest side has a measurement of x. What is the measurement of the other side that includes _ the right angle? A x √2 B 30x C 2x _ D x √3
entify and apply patterns from right triangles to ecial right triangles (45-45-90 and 30-60-90) and iples.
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h2 = ! h2 = !2 _ ! = h √2 _ h = ! √2
5 A wire from the top of a transmission tower to the ground is 250 feet long. The wire makes a 45° angle with the ground. About how tall is the transmission tower? A 167.8 ft B 176.8 ft C 186.7 ft
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4 Brett built a skateboard ramp that was a triangle with angles of 45°, 45°, and 90°. If the height of the ramp is h, which formula tells him the length, !, of the skateboard ramp?
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5 A wire from the top of a transmission tower to the ground is 250 feet long. The wire makes a 45° angle with the ground. About how tall is the transmission tower? A 167.8 ft B 176.8 ft C 186.7 ft D 187.6 ft
midpoint. Read each question and choose the 11 best answer.
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1 In San Antonio, Megan’s family walks from the Instituto Cultural Mexicano to the Spanish Governor’s Palace. If the two were plotted on a coordinate plane, the Instituto might be at (0, 1) and the palace at (-2, 0), with 1 unit equaling 1 block. If Megan could take a bird’s straight flight path from one site to the other, what would the distance be? A 1.41 blocks C 2.24 blocks B 1.73 blocks D 2.42 blocks 2 After seeing the Four Seasons Garden at Fort Worth, Justin decides that a four seasons garden would make a perfect wedding present for his older sister. He plans the garden as shown, with the coordinates (6,5.5) and (2.5,5) marking a line that forms the diameter of the garden. (6, 5.5) Daylily
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3 Padma wants to build an arbor across a sidewalk that angles from her house to the street. When she lays out the plot plan for the house and grounds, the endpoints of the sidewalk are located at (-5, -2) and (6, 3), as shown. (6, 3)
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The arbor will be built at the midpoint of the sidewalk’s length. Which coordinate pair marks the midpoint? A (0.5, 2.5) C (1, 1) B (0.5, 0.5) D (5.5, 2.5) 4 The diameter of a circle is shown below. ( 8, 4)
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4 The diameter of a circle is shown below. ( 8, 4)
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What is the length of the circle’s diameter? F 6.71 units H 10.82 units G 8.24 units J 12.37 units
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pair marks the midpoint? A (0.5, 2.5) C (1, 1) B (0.5, 0.5) D (5.5, 2.5)
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Read each question and choose the best answer.
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1 Lourdes works at a frame shop after school. She put together 4 frames. All corners need to measure 90°. Which of the four frames has corners that all measure 90°? A
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Using the Pythag coordinates for v right triangle? F (1, 4) G (0.577, -0.1
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3 Amber wants to Corpus Christi to An Internet sear between Corpus and between Gal notices that the 3 shown.
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What does Amb approximate dist Christi and Waco A 112 mi B 196 mi
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Using the Pythagorean Theorem, which coordinates for vertex R would create a right triangle? F (1, 4) H (0.577, -0.288) G (0.577, -0.115) J (-5, -3) 3 Amber wants to drive from her home in Corpus Christi to visit a friend in Waco. An Internet search turns up the distances between Corpus Christi and Galveston and between Galveston and Waco. Amber notices that the 3 cities form a triangle as shown. Texas
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3 Amber wants to drive from her home in Corpus Christi to visit a friend in Waco. An Internet search turns up the distances between Corpus Christi and Galveston and between Galveston and Waco. Amber notices that the 3 cities form a triangle as shown.
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What does Amber estimate as the approximate distance between Corpus Christi and Waco? A 112 mi C 278 mi B 196 mi D 392 mi
Copyright Š Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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right triangle? F (1, 4) H (0.577, -0.288) G (0.577, -0.115) J (-5, -3)
Read each question and choose the best answer. 17 1 A triangle has sides_of the following lengths: 150, 150 √2, and 150 millimeters. Which of the following triangles could NOT be similar to this triangle? A a triangle with 2 equal sides 2 inches long B a triangle with 1 side with a length of 20 meters, 1 angle of 90°, and a hypotenuse of 28.28 meters C a triangle with two 45° angles D a triangle with a right angle and another angle of 30° 2 Amir and his brother each build ramps for their bikes on the family property. Each ramp includes one 90° angle, as shown.
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C a triangle with two 45° angles D a triangle with a right angle and another angle of 30°
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2 Amir and his brother each build ramps for their bikes on the family property. Each ramp includes one 90° angle, as shown.
One brother decides to build a steeper ramp with a 45° slope. Which describes the steeper ramp? _ F a ramp with the length equal to √2 times its height from the_ground. G a ramp with sides of 4 √3, 4, and 8 H a ramp with one side 2 times the length of the other J a ramp with one 30° angle
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3 A right triangle has sides of 3, 4, and 5 centimeters. Which triangle would be similar? A a triangle with two 60° angles B a right triangle with sides of 50, 80, and 94.34 cm C a right triangle with sides of 45, 60, and 75 in. D a right triangle with sides of 3, 5, and 5.83 ft 4 Two right triangles have sides that are Pythagorean triples. Which other condition or conditions must exist for them to be similar to each other? F None, since all triangles with sides that are Pythagorean triples are similar to each other. G If one has sides of lengths a, b, and c, the other must have sides of ka, kb, and
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1 In San Antonio, Megan’s family walks (6, 3) from the Instituto Cultural Mexicano to the Spanish Governor’s Palace. If the two were plotted on a coordinate plane, the Instituto might be at (0, 1) and the palace at (-2, 0), with 1 unit equaling 1 block. ( 5, 2) If Megan could take a bird’s straight flight path from one site to the other, what would the distance be? The arbor will be built the blocks midpoint of A 1.41 blocks C at2.24 the sidewalk’s coordinate B 1.73 blockslength.DWhich 2.42 blocks pair marks the midpoint? & A (0.5, 2.5) C (1, 1) & 2 After seeing the Four Seasons Garden B (0.5, 0.5) D (5.5, 2.5) at Fort Worth, Justin decides that a four 4.& seasons garden would make a perfect 4 The diameter of afor circle is shown below. wedding present his older sister. He plans the garden as shown, with the ( 8, 4) coordinates (6,5.5) and (2.5,5) marking a line that forms the diameter of the garden. (6, 5.5)
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midpoint. street. When she lays out the plot plan for the house and grounds, the endpoints of Read each question and choose the the sidewalk are located at (-5, -2) and best answer. (6, 3), as shown. 3.&&
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