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mathematics
holt mcdougal larson geometry
Holt McDougal Larson Geometry 1st Edition Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff - Solutions
For any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. LL LM
A quadrilateral that has exactly one pair of parallel sides and diagonals that are congruent is a (n) _____?______.
What property of a parallelogram is included in the definition of a parallelogram? What properties are described by the theorems in this lesson?
Explain how knowing that AB∣∣CD and AD∣∣BC allows you to show that quadrilateral ABCD is a parallelogram.
Find the value of each variable in the parallelogram. X 15 9
Describe the differences between a kite and a trapezoid.
A student claims that because two pairs of sides are congruent, quadrilateral DEFG shown at the right is a parallelogram. Describe the error that the student is making. G 7 7 D 5 5 E F DEFG is a parallelogram. x
Describe three methods you could use to prove that a parallelogram is a rhombus.
A quadrilateral has four congruent sides. Is the quadrilateral a parallelogram? Justify your answer.
Find the sum of the measures of the interior angles of the indicated convex polygon.Nonagon
For any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. LK= LM
How many exterior angles are there in an n-gon? Are all the exterior angles considered when you use the Polygon Exterior Angles Theorem? Explain.
Copy the chart. Put an X in the box if the shape always has the given property. Property Both pairs of opp. sides are =. ? Rectangle Rhombus Square Kite Trapezoid ? ? ? ? ? דיי
Find the value of each variable in the parallelogram. 6 n m+1 12
What theorem can you use to show that the quadrilateral is a parallelogram? 100⁰ 100°
For any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. JK = KL
Copy the chart. Put an X in the box if the shape always has the given property. Property Both pairs of opp. sides are ||. ? Rectangle Rhombus Square Kite Trapezoid ? ? ? ? ?
What theorem can you use to show that the quadrilateral is a parallelogram? # +
Find the value of each variable in the parallelogram. 55° aº
What theorem can you use to show that the quadrilateral is a parallelogram? 14, 20 20 14
Find the sum of the measures of the interior angles of the indicated convex polygon.14-gon
For any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. JM = KL
Copy the chart. Put an X in the box if the shape always has the given property. Property Exactly 1 pair of opp. sides are ||. ? סיי Rectangle Rhombus Square Kite Trapezoid ? ? ? ? ?
Find the value of each variable in the parallelogram. 2pº 120⁰
Find m∠J, m∠L, and m∠M. K 50° J M L
Find the sum of the measures of the interior angles of the indicated convex polygon.16-gon
Find the sum of the measures of the interior angles of the indicated convex polygon.20-gon
For any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. JL = KM
Copy the chart. Put an X in the box if the shape always has the given property. Property All / are =. 0 ? Rectangle Rhombus Square Kite Trapezoid ? ? ? ? ?
Find the value of each variable in the parallelogram. 20 105° (d-21) Z-8
For any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. LW = LX M7
The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides.360°
For what value of x is the quadrilateral a parallelogram? 2x + 3 x+7
Find the measure of the indicated angle in the parallelogram. Find mL B. A 51° B D C
For what value of x is the quadrilateral a parallelogram? 6x 3x + 2
Find the measure of the indicated angle in the parallelogram. Find mLL. M L 95° N P
Determine whether the quadrilateral is a trapezoid. Explain. A D B J C
For any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. WX = YZ
The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram. A(0, 1), B(4, 4), C(12, 4), D(8, 1)
The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram. A(-3, 0), B(-3, 4), C(3, -1), D(3, -5)
Determine whether the quadrilateral is a trapezoid. Explain. H 130° G
For any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. WX = XY
Find the measure of the indicated angle in the parallelogram. Find mL Y. W Z 119° X Y
Determine whether the quadrilateral is a trapezoid. Explain. M L ·K
For any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. WY=XZ
The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides.2340°
Describe and correct the error in classifying the quadrilateral. D 59° 125% B 55% LB and LC are supplements, so AB CD. So, ABCD is a parallelogram. x
Find m ∠ J, m ∠ L, and m ∠ M. K 118° M
For any rhombus JKLM, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. LJKM LLKM
For what value of x is the quadrilateral a parallelogram? 4x + 2 + 5x-6
Find the value of each variable in the parallelogram. (g+ 4)° 7 65° 16-h
Copy the chart. Put an X in the box if the shape always has the given property. Property Exactly 1 pair of opp. / are =. ? Rectangle Rhombus Square Kite Trapezoid ? ? ? ? ?
The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides.1980°
Find m ∠ J, m ∠ L, and m ∠ M. M 100° K L
The sum of the measures of the interior angles of a convex polygon is given. Classify the polygon by the number of sides.720°
Which additional information would not be enough to solve ΔPRQ? P Q -R
A ramp is used to launch a kayak. What is the height of an 11 foot ramp when its angle is 30 as shown? h ft 11 ft 30°
Graph points A, B, and C. Connect the points to form ΔABC. Decide whether ΔABC is acute, right, or obtuse. A(-2, 4), B(6, 0), C(-5, -2)
Classify the quadrilateral. Explain your reasoning.
Find the unknown side length. Then find sin X and cos X. Write each answer as a fraction in simplest form and as a decimal. Round to four decimal places, if necessary. X 65 56 Y
Find y. Then find z. Round to the nearest tenth. 30° 150 у Z 40°
Graph points A, B, and C. Connect the points to form ΔABC. Decide whether ΔABC is acute, right, or obtuse. A(0, 2), B(5, 1), C(1, -1)
Find y. Then find z. Round to the nearest tenth. 45° 82 у 28° Z
The peak of the doghouse shown forms a right angle. Use the given dimensions to find the height of the roof. 1.5 ft 1.5 ft
You want to determine the height of a monument at a local park. You use a cardboard square to line up the top and bottom of the monument. Mary measures the vertical distance from the ground to your eye and the distance from you to the monument. Approximate the height of the monument (as shown at
In Exercises 29 and 30, solve for x. 36 39 6 10 9
In Exercises 30 and 31, copy and complete the statement with , or =, if possible. If it is not possible, explain why. mLA ? mLD
In Exercises 29 and 30, solve for x. 13 X -14- 15
Find the perimeter of the figure at the right, where AC = 26, AD = BF, and D is the midpoint of AC. E 50° A D C 35% G B F H
Draw a right isosceles triangle and label the two leg lengths x. Then draw the altitude to the hypotenuse and label its length y. Now draw the three similar triangles and label any side length that is equal to either x or y. What can you conclude about the relationship between the two smaller
Solve for x if the lengths of the two legs of a right triangle are 2x and 2x + 4, and the length of the hypotenuse is 4x - 4.
Find the approximate perimeter of the figure. 55° H 60° 55° -1.5 cm
A roller coaster makes an angle of 52° with the ground. The horizontal distance from the crest of the hill to the bottom of the hill is about 121 feet, as shown. Find the heighth of the roller coaster to the nearest foot. 52° 121 ft h
A surveyor is standing 118 feet from the base of the Washington Monument. The surveyor measures the angle between the ground and the top of the monument to be 78°. Find the height h of the Washington Monument to the nearest foot.
Tell whether a triangle with side lengths 5x, 12x, and 13x (where x > 0) is acute, right, or obtuse.
In baseball, the distance of the paths between each pair of consecutive bases is 90 feet and the paths form right angles. How far does the ball need to travel if it is thrown from home plate directly to second base?
Find the length of the midsegment of the trapezoid. M 18 10 N
Describe how to prove that ABCD is a parallelogram. D A C B
Find the length of the midsegment of the trapezoid. 57 M N 76
For any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. LWXZ = LYXZ
Find the value of each variable in the parallelogram. 16 2n 9-n 4m
Give the most specific name for the quadrilateral. Explain. M K L
What is the most specific name for the quadrilateral shown at the right?
Find the length of the midsegment of the trapezoid. M 21 25 N
The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram. A(-5, 0), B(0, 4), C(3, 0), D(-2,-4)
Find the value of each variable in the parallelogram. 15 9 b-1 5a
For any rectangle WXYZ, decide whether the statement is always or sometimes true. Draw a diagram and explain your reasoning. WY 1 XZ
The vertices of quadrilateral ABCD are given. Draw ABCD in a coordinate plane and show that it is a parallelogram. A(-2, 3), B(-5, 7), C(3, 6), D(6,2)
Each half of the drawbridge is about 284 feet long, as shown. How high does a seagull who is on the end of the drawbridge rise when the angle with measure x° is 30°? 45°? 60°? 284 ft
What is the area of a right triangle with a leg length of 15 feet and a hypotenuse length of 39 feet? A 270 ft² B 292.5 ft² C 540 ft² (D 585 ft²
Find y. Then find z. Round to the nearest tenth. 42° N -120 у
Use the Geometric Mean Theorems to find AC and BD. A 20 в 15 D C
Find the unknown side length. Then find sin X and cos X. Write each answer as a fraction in simplest form and as a decimal. Round to four decimal places, if necessary. X 30 16 Z
Find the unknown side length x. Write your answer in simplest radical form. 5 3 X 7
Find the perimeter of the triangle. Round to the nearest tenth. 68° 15
Tell whether the triangle is a right triangle. If so, find the length of the altitude to the hypotenuse. Round decimal answers to the nearest tenth. 14 4 V 33 18
Find the unknown side length. Then find sin X and cos X. Write each answer as a fraction in simplest form and as a decimal. Round to four decimal places, if necessary. Y N 3√5 6 X
A student tells you that if you double all the sides of a right triangle, the new triangle is obtuse. Explain why this statement is incorrect.
What type of triangle has side lengths of 4, 7, and 9? A Acute scalene C Obtuse scalene B Right scalene None of the above
Find the value of each variable. Write your answers in simplest radical form. 30° 8 X y 60°
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