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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
Find the unknown measure. L M 60° 60° 16 N
In Exercises 37 and 38, write a proof. GIVEN ▶ JM = LM PROVE K L AJKM = ALKM M
Use the information in the diagram to find the measure. Find mLABD. D C A 20° B
Use a ruler and protractor to draw the given type of triangle. Mark the largest angle and longest side in red and the smallest angle and shortest side in blue. What do you notice?Acute scalene
List the sides and the angles in order from smallest to largest. R 6 T 10 9 S
Which is a possible measure for ∠JKM? K 25° L 8 M 6 J
In the diagram at the right, P is the centroid of ΔRST. If LS 36, find PL and PS. =
In ΔXYZ, XJ ≅ JY, YL ≅ LZ, and XK ≅ KZ. Copy and complete the statement. XY ?
Point P is inside ΔABC and is equidistant from points A and B. On which of the following segments must P be located? A AB The midsegment opposite AB The perpendicular bisector of AB D The perpendicular bisector of AC
Can you conclude that EH bisects ∠FEG? Explain. H F G E
Find the coordinates of the centroid P of ΔABC. A(-1, 2), B(5, 6), C(5,-2)
List the sides and the angles in order from smallest to largest. J 28 25 K 13 L
In the diagram at the right, P is the centroid of ΔRST. If TP = 20, find TJ and PJ.
In ΔXYZ, XJ ≅ JY, YL ≅ LZ, and XK ≅ KZ. Copy and complete the statement. YJ = ? = ?
In ΔXYZ, XJ ≅ JY, YL ≅ LZ, and XK ≅ KZ. Copy and complete the statement. JL = ? ??
Explain why the conclusion is not correct given the information in the diagram. A E B x AB will pass through C.
The path from E to F is longer than the path from E to D. The path from G to D is the same length as the path from G to F. What can you conclude about the angles of the paths? Explain your reasoning. D E G F
In the diagram at the right, P is the centroid of ΔRST. If JR = 25, find JS and RS.
Can you conclude that EH bisects ∠FEG? Explain. H F G E
Find the coordinates of the centroid P of ΔABC. A(0, 4), B(3, 10), C(6, -2)
List the sides and the angles in order from smallest to largest. M 127° N 29° P
Can you conclude that EH bisects ∠FEG? Explain. H F G E
In ΔXYZ, XJ ≅ JY, YL ≅ LZ, and XK ≅ KZ. Copy and complete the statement. JK = ? fino ?
In Exercises 11-15, use the diagram. JN is the perpendicular bisector of MK.Find NM. 7y-6 M 5y + 8 N 35 P 9y-13 K -7y+1 L
List the sides and the angles in order from smallest to largest. D 33° G
In Exercises 11-15, use the diagram. JN is the perpendicular bisector of MK.Find JK. 7y-6 M 5y + 8 N 35 P 9y-13 K -7y + 1 L
In Exercises 11-15, use the diagram. JN is the perpendicular bisector of MK. Is L on JP? Explain your reasoning.
Explain why the student's reasoning is not correct. P 44° 46° Q x R By the Hinge Theorem, PQ < SR.
In Exercises 11 and 12, write a temporary assumption you could make to prove the conclusion indirectly.If x and y are odd integers, then xy is odd.
IS BD a perpendicular bisector of ΔABC? Is BD a median? an altitude? В C D A
Draw a large right triangle and find its centroid.
In Exercises 11-15, use the diagram. JN is the perpendicular bisector of MK.Find ML. 7y-6 M 5y + 8 N 35 P 9y - 13 K 7y + 1 L
In Exercises 11-15, use the diagram. JN is the perpendicular bisector of MK.Find KL. 7y-6 M 5y + 8 N 35 P 9y-13 K +7y + 1 L
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Isosceles right triangle: leg length is 7 units
In the diagram, the perpendicular bisectors of ΔABC meet at point G and are shown in blue. Find the indicated measure. Find BG. A D 6, 9 B 3 G F E C
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Scalene triangle: one side length is 2m
IS BD a perpendicular bisector of ΔABC? Is BD a median? an altitude? A D В C
Explain why the student's reasoning is not correct. T U 57° 56° W x X By the Hinge Theorem, XW < XY.
IS BD a perpendicular bisector of ΔABC? Is BD a median? an altitude? В DE С
In Exercises 11 and 12, write a temporary assumption you could make to prove the conclusion indirectly.In ΔABC, if m∠A = 100°, then ∠B is not a right angle.
Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. 13 12 15 (2x + 5)° 66° 12
Can you find the value of x? Explain. 3 X
Can you find the value of x? Explain. 40° x
Draw a large obtuse, scalene triangle and find its orthocenter.
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex.Right triangle: leg lengths are 3 units and 2 units
Your study partner is planning to write an indirect proof to show that ∠A is an obtuse angle. She states "Assume temporarily that ∠A is an acute angle." What has your study partner overlooked?
Is it possible to construct a triangle with the given side lengths? If not, explain why not. 6, 7, 11
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Rectangle: length is a and width is b
Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. 3 3x + 2 110° 27° 102° x +3 3
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex.Square: side length is 3 units
Use the diagram shown and the given information to decide whether YW is a perpendicular bisector, an angle bisector, a median, or an altitude of ∆XYZ. There may be more than one right answer. YW L XZ and XW = ZW
Use the diagram shown and the given information to decide whether YW is a perpendicular bisector, an angle bisector, a median, or an altitude of ∆XYZ. There may be more than one right answer. XW = ZW
Use the diagram shown and the given information to decide whether YW is a perpendicular bisector, an angle bisector, a median, or an altitude of ∆XYZ. There may be more than one right answer. LXYW = LZYW
Find the indicated measure. Point L is the incenter of AEGJ. Find HL. E F 17 G L 15 K H J
What is the value of x in the diagram? -(3x - 9)°
Is it possible to construct a triangle with the given side lengths? If not, explain why not. 35, 120, 125
Is it possible to construct a triangle with the given side lengths? If not, explain why not. 28, 34, 39
Find the indicated measure. Point D is the incenter of AXYZ. Find DB. X D 9 C B -15 Z
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Right triangle: leg lengths are r and s
Is it possible to construct a triangle with the given side lengths? If not, explain why not. 3, 6, 9
Use the Hinge Theorem or its converse and properties of triangles to write and solve an inequality to describe a restriction on the value of x. A 4x-3 в 2x С
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Isosceles right triangle: leg length is p
In the diagram, the perpendicular bisectors of ΔABC meet at point G and are shown in blue. Find the indicated measure. Find GA. A 1 D G F B 11 9 E C 70
Place the figure in a coordinate plane in a convenient way. Assign coordinates to each vertex. Square: side length is s
Can you find the value of x? Explain. 7 Xx
Draw a right triangle. Use a compass and straightedge to find its circumcenter. Use a compass to draw the circumscribed circle.
Find the measurements. Explain your reasoning. Given that DBL AC, find DC and m2 ABD.
In the diagram, N is the incenter of ΔGHJ. Which statement cannot be deduced from the given information? J G N K M H
Sketch ΔABC. Find the length and the slope of each side. Then find the coordinates of each midpoint. Is ΔABC a right triangle? Is it isosceles? Explain. (Assume all variables are positive, p ≠ q, and m ≠ n.) A(0, n), B (m, n), C(m, 0)
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.3 meters, 4 meters
Use the diagram shown and the given information to decide whether YW is a perpendicular bisector, an angle bisector, a median, or an altitude of ∆XYZ. There may be more than one right answer. YW L XZ and XY = ZY
Describe the error in reasoning. Then state a correct conclusion about distances that can be deduced from the diagram. W ||| T X Z Y TV = TZ x
Two hikers start at the visitor center. The first hikes 4 miles due west, then turns 40 toward south and hikes 1.8 miles. The second hikes 4 miles due east, then turns 52 toward north and and hikes 1.8 miles. Which hiker is farther from the visitor center? Explain how you know. 4 miles 4 miles
Use the diagram shown and the given information to decide whether YW is a perpendicular bisector, an angle bisector, a median, or an altitude of ∆XYZ. There may be more than one right answer. ΔXYW = ΔZYW
Sketch ΔABC. Find the length and the slope of each side. Then find the coordinates of each midpoint. Is ΔABC a right triangle? Is it isosceles? Explain. (Assume all variables are positive, p ≠ q, and m ≠ n.) A(0, 0), B(h, h), C(2h, 0)
Describe the error in reasoning. Then state a correct conclusion about distances that can be deduced from the diagram. B A G F E GD = GF x
Sketch ΔABC. Find the length and the slope of each side. Then find the coordinates of each midpoint. Is ΔABC a right triangle? Is it isosceles? Explain. (Assume all variables are positive, p ≠ q, and m ≠ n.) A(0, 0), B(p, q), C(2p, 0)
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.5 inches, 12 inches
Which group of side lengths can be used to construct a triangle? A 3 yd, 4 ft, 5 yd C 11 in., 16 in., 27 in. B 3 yd, 5 ft, 8 ft D 2 ft, 11 in., 12 in.
Copy and complete the statement with always, sometimes, or never. Justify your answer. The circumcenter of a scalene triangle is_?__ inside the triangle.
Prove the perpendicular Bisector Theorem. GIVEN CP is the perpendicular bisector of AB. PROVE CA = CB Plan for Proof Show that right triangles AAPC and ABPC are congruent. Then show that CA = CB. A P B
Find the value of x that makes N the incenter of the triangle. A 37 35 N K B -2x L C
Find the measurements. Explain your reasoning. Given that AD = DC, find mL ADB and m2 ABD.
Use ΔGHJ, where A, B, and C are midpoints of the sides. If AC = 3y - 5 and HJ = 4y + 2, what is HB?
A scissors lift can be used to adjust the height of a platform. L M
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 10 yards, 23 yards
A cable-stayed bridge is shown below. Two cable lengths are given. Find the lengths of the blue cables. Justify your answer. 59.6 m -128 m- 195.5 m -40 m +40m+ 128 m-
Find the value of x that makes N the incenter of the triangle. R G -14x F N Q H 25 24 P
Copy and complete the statement for ΔDEF with medians DH, EJ, and FG, and centroid K. EJ = ? KJ
Use ΔGHJ, where A, B, and C are midpoints of the sides. If GH = 7z 1 and BC = 4z - 3, what is GH?
You and two friends plan to walk your dogs together. You want your meeting place to be the same distance from each person's house. Explain how you can use the diagram to locate the meeting place. your house Mike's house Ken's house
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 25 meters, 25 meters
Copy and complete the statement for ΔDEF with medians DH, EJ, and FG, and centroid K. DK=? KH
Copy and complete the statement for ΔDEF with medians DH, EJ, and FG, and centroid K. FG= ? KF
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.2 feet, 40 inches
Archaeologists find three stones. They believe that the stones were once part of a circle of stones with a community firepit at its center. They mark the locations of Stones A, B, and Con a graph where distances are measured in feet.a. Explain how the archaeologists can use a sketch to estimate the
Explain why the conclusion is incorrect. B y 1.0 5 10 E C DE = 1/BC, so by the Midsegment Theorem AD = DB and AE = EC. x
Point D is the incenter of ΔABC. Write an expression for the length x in terms of the three side lengths AB, AC, and BC. B A X/ D C
In a field hockey game, the goalkeeper is at point G and a player from the opposing team hits the ball from point B. The goal extends from left goalpost L to right goalpost R. Will the goalkeeper have to move farther to keep the ball from hitting L or R? Explain. G R B
You are constructing a fountain in a triangular koi pond. You want the fountain to be the same distance from each edge of the pond. Where should you build the fountain? Explain your reasoning. Use a sketch to support your answer.
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