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mathematics
holt mcdougal larson geometry

Questions and Answers of Holt McDougal Larson Geometry

The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure. RP
In Exercises 29-31, determine whether there is enough information to prove that JKLM is an isosceles trapezoid. Explain. GIVEN ► JK|| LM, ZJML = Z KLM, m/KLM + 90° K M L
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC = 53° and DE = 8, find the indicated measure. mL AED
In the diagram, QRST and STUV are parallelograms. Find the values of x and y. Explain your reasoning. Q 20 R T 40° U y° X 80° S V
What type of special quadrilateral is outlined?
The diagonals of a rhombus are 6 inches and 8 inches. What is the perimeter of the rhombus? Explain.
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC = 53° and DE = 8, find the indicated measure. ᎠᏴ
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC = 53° and DE = 8, find the indicated measure. mLADC
The measure of one interior angle of a parallelogram is 0.25 times the measure of another angle. Find the measure of each angle.
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC = 53° and DE = 8, find the indicated measure. AE
A student claims incorrectly that the marked information can be used to show that the figure is a parallelogram. Draw a quadrilateral with the marked properties that is clearly not a parallelogram.
A student claims incorrectly that the marked information can be used to show that the figure is a parallelogram. Draw a quadrilateral with the marked properties that is clearly not a parallelogram.
The base of a jewelry box is shaped like a regular hexagon. What is the measure of each interior angle of the hexagon?
In the photograph of a chest of drawers, HC is the midsegment of trapezoid ABDG, GD is the midsegment of trapezoid HCEF, AB = 13.9 centimeters, and GD = 50.5 centimeters. Find HC. Then find FE.
What type of special quadrilateral is outlined?
The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure. mL SRT
What type of special quadrilateral is outlined? x+2 X X Xx+2
The measure of one interior angle of a parallelogram is 50 degrees more than 4 times the measure of another angle. Find the measure of each angle.
The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure. m2 QPR
The diagonals of rhombus ABCD intersect at E. Given that m∠BAC = 53° and DE = 8, find the indicated measure. AC
Draw a rectangle and bisect its angles. What type of quadrilateral is formed by the intersecting bisectors? Justify your answer.
Explain why a kite and a general quadrilateral are the only quadrilaterals that can be concave.
A student claims incorrectly that the marked information can be used to show that the figure is a parallelogram. Draw a quadrilateral with the marked properties that is clearly not a parallelogram.
The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure. QP
The diagram shows the mechanism for opening the canopy on a small airplane. Two pivot arms attach at four pivot points A, B, C, and D. These points form the vertices of a parallelogram. Find m∠D
Find m∠1 and m∠2. Explain your reasoning. 1 98° 2
In the diagram below, BG is the midsegment of ΔACD and GE is the midsegment of ΔADF. Explain why the midsegment of trapezoid ACDF is parallel to each base and why its length is one half the sum of
The mirror shown is attached to the wall by an arm that can extend away from the wall. In the figure, points P, Q, R, and S are the vertices of a parallelogram. This parallelogram is one of several
Find m∠1 and m∠2. Explain your reasoning. 150° 1 2
The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure. QR
What special type of quadrilateral is EFGH? Write a paragraph proof to show that your answer is correct. GIVEN PQRS is a square. E, F, G, and H are midpoints of the sides of the square. PROVE EFGH is
In the diagram, the midpoints of the sides of a quadrilateral have been joined to form what appears to be a parallelogram. Show that a quadrilateral formed by connecting the midpoints of the sides of
The diagonals of rectangle QRST intersect at P. Given that m∠PTS = 34° and QS = 10, find the indicated measure. RS
What special type of quadrilateral is EFGH? Write a paragraph proof to show that your answer is correct. GIVEN ▶ In the three-dimensional figure, JK= LM; E, F, G, and H are the midpoints of JL, KL,
Find m∠1 and m∠2. Explain your reasoning. 2 1/126°
In Exercises 43 and 44, use the diagram.Find the values of x and y. Explain your reasoning. B y A 7 x+3 С
Use the diagram to complete the proportion. ? AB AC AB
The diagonals of square LMNP intersect at K. Given that LK = 1, find the indicated measure. m/LMK
The diagonals of square LMNP intersect at K. Given that LK = 1, find the indicated measure. mLMKN
Use the diagram to complete the proportion. AB - BD ВС 2
Draw a triangle. Copy the triangle and combine the two triangles to form a quadrilateral. Show that the quadrilateral is a parallelogram. Then show how you can make additional copies of the triangle
Suppose you choose a point on the base of an isosceles triangle. You draw segments from that point perpendicular to the legs of the triangle. Prove that the sum of the lengths of those segments is
The diagonals of square LMNP intersect at K. Given that LK = 1, find the indicated measure. mLLPK
Let ∠A be an acute angle in a right triangle. Approximate the measure of ∠A to the nearest tenth of a degree. sin A = 0.77
Quadrilaterals JKLM and PQRS are similar. If JK = 3.6 centimeters and PQ = 1.2 centimeters, find the scale factor of JKLM to PQRS.
Let ∠A be an acute angle in a right triangle. Approximate the measure of ∠A to the nearest tenth of a degree. cos A = 0.81
Use the diagram of ▱WXYZ to find the indicated length. YZ
In Exercises 43-45, draw a figure that fits the description.A quadrilateral that is equilateral but not equiangular.
Let ∠A be an acute angle in a right triangle. Approximate the measure of ∠A to the nearest tenth of a degree. sin A = 0.35
Use the diagram of ▱WXYZ to find the indicated length. WZ
Three of the vertices of ▱ABCD are given. Find the coordinates of point D. Show your method. A(-1, -2), B(4, -2), C(6, 2), D(x, y)
The diagonals of square LMNP intersect at K. Given that LK = 1, find the indicated measure. KN
Quadrilaterals ABCD and EFGH are similar. The scale factor of ABCD to EFGH is 8 : 5, and the perimeter of ABCD is 90 feet. Find the perimeter of EFGH.
Use the diagram of ▱WXYZ to find the indicated length. XV
In Exercises 43-45, draw a figure that fits the description.A quadrilateral that is equiangular but not equilateral.
Place a right triangle in a coordinate plane in a way that is convenient for finding side lengths. Assign coordinates to each vertex.
The diagonals of square LMNP intersect at K. Given that LK = 1, find the indicated measure. LP
The diagonals of square LMNP intersect at K. Given that LK = 1, find the indicated measure. MP
Use the diagram of ▱WXYZ to find the indicated length. XZ
In Exercises 43-45, draw a figure that fits the description.A quadrilateral that is concave.
Let ∠A be an acute angle in a right triangle. Approximate the measure of ∠A to the nearest tenth of a degree. cos A = 0.23
Three of the vertices of ▱ABCD are given. Find the coordinates of point D. Show your method. A(1, 4), B(0, 1), C(4, 1), D(x, y)
Decide if the side lengths form a triangle. If so, would the triangle be acute, right, or obtuse? 5, 9, and V106
Find the sine and cosine of the indicated angle. Write each answer as a fraction and a decimal. ZR
Decide if the side lengths form a triangle. If so, would the triangle be acute, right, or obtuse?9, 13, and 6
Decide if the side lengths form a triangle. If so, would the triangle be acute, right, or obtuse?10, 12, and 7
Decide if the side lengths form a triangle. If so, would the triangle be acute, right, or obtuse?8, 12, and 4
Decide if the side lengths form a triangle. If so, would the triangle be acute, right, or obtuse?24, 10, and 26
Decide if the side lengths form a triangle. If so, would the triangle be acute, right, or obtuse?9, 10, and 11
You want to mark off a square region in your yard for a patio. You use a tape measure to mark off a quadrilateral on the ground. Each side of the quadrilateral is 2.5 meters long. Explain how you can
Write the corollary as a conditional statement and its converse. Then explain why each statement is true.Rhombus Corollary.
Write the corollary as a conditional statement and its converse. Then explain why each statement is true.Rectangle Corollary.
Write the corollary as a conditional statement and its converse. Then explain why each statement is true.Square Corollary.
In ΔAJKL, KL = 54.2 centimeters. Point M is the midpoint of JK and Nis the midpoint of JL. Find MN.
Find the sine and cosine of the indicated angle. Write each answer as a fraction and a decimal. ZT
You tie an apple balloon to a stake in the ground. The rope is 10 feet long. As the wind picks up, you observe that the balloon is now 6 feet away from the stake. How far above the ground is the
Use the diagram.a. Name all the altitudes in ΔEGF. Explain. b. Find FH. c. Find the area of the triangle. F E 5 H 7 G
The side lengths of a triangle are 6, 8, and x (where x > 0). What are the values of x that make the triangle a right triangle? an acute triangle? an obtuse triangle?
You are creating a quilt that will have a traditional "flying geese" border, as shown below.a. Find all the angle measures of the small blue triangles and the large orange triangles. b. The width of
Three side lengths of a right triangle are 25, 65, and 60. Explain how you know which side is the hypotenuse.
The airplane door is 19 feet off the ground and the ramp has a 31° angle of elevation. What is the length y of the ramp? 31° 19 ft
The sides of a triangle have lengths x, x + 4, and 20. If the length of the longest side is 20, what values of x make the triangle acute?
Use the diagram.a. Sketch the three similar triangles in the diagram. Label the vertices. Explain how you know which vertices correspond. b. Write similarity statements for the three triangles. c.
In your town, there is a field that is in the shape of a right triangle with the dimensions shown.a. Find the perimeter of the field. b. You are going to plant dogwood seedlings about every ten feet
Find the horizontal distance h the bleachers cover. Round to the nearest foot. 27° 18 ft hft
A soccer ball is placed 10 feet away from the goal, which is 8 feet high. You kick the ball and it hits the crossbar along the top of the goal. What is the angle of elevation of your kick?
Write expressions for the tangent of each acute angle in the triangle. Explain how the tangent of one acute angle is related to the tangent of the other acute angle. What kind of angle pair are ∠A
As you are gathering leaves for a science project, you look back at your campsite and see that the campfire is not completely out. You want to get water from a nearby river to put out the flames with
You are making a canvas frame for a painting using stretcher bars. The rectangular painting will be 10 inches long and 8 inches wide. Using a ruler, how can you be certain that the corners of the
You are standing on a footbridge in a city park that is 12 feet high above a pond. You look down and see a duck in the water 7 feet away from the footbridge. What is the angle of depression? Explain
You are flying a kite with 20 feet of string extended. The angle of elevation from the spool of string to the kite is 41°.a. Draw and label a diagram to represent the situation. b. How far off
Name each quadrilateral-parallelogram, rectangle, rhombus, and square-for which the statement is true.It is equiangular and equilateral.
In the diagram, BD is the perpendicular bisector of AC.Which pairs of segment lengths are equal? 22 - A x+7 2x + 6 B 16 C
You are looking at an eye chart that is 20 feet away. Your eyes are level with the bottom of the "E" on the chart. To see the top of the "E," you look up 1°. How tall is the "E"? 1° 20 ft E 1 FP 2
You want to hang a banner that is 29 feet tall from the third floor of your school. You need to know how tall the wall is, but there is a large bush in your way.a. You throw a 38 foot rope out of the
You walk 749 feet due east to the gym from your home. From the gym you walk 800 feet southwest to the library. Finally, you walk 305 feet from the library back home. Do you live directly north of the
The road salt shown is stored in a cone-shaped pile. The base of the cone has a circumference of 80 feet. The cone rises at an angle of 32°. Find the height h of the cone. Then find the length s of
According to the Americans with Disabilities Act, a ramp cannot have an incline that is greater than 5°. The regulations also state that the maximum rise of a ramp is 30 inches. When a ramp needs to
In the diagram, BD is the perpendicular bisector of AC.What is the value of x? 22 - 2 x+7 A 2x + 6 D B 16 С
Give the most specific name for the quadrilateral. Explain. P₁ S 111° Q R

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