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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 coordinates of the red point(s) in the figure. Then show that the given statement is true. ΔΟΡQ = ΔRSQ P(?, ?) 0(0, 0) alh, k) R(2h, 2k) IS(2h, k)
Use a compass and a straightedge to draw ΔABC with incenter D. Label the angle bisectors and the perpendicular segments from D to each of the sides of ΔABC. Measure each segment. What do you notice? What theorem have you verified for your ΔABC?
Find the coordinates of the red point(s) in the figure. Then show that the given statement is true. slope of HE = -(slope of DG) H(?, ?) D(-2h, 0) A(0, 2k) G(?, ?) E(2h, 0) X
A rectangle with side lengths 3h and k has a vertex at (-h, k). Which point cannot be a vertex of the rectangle? A (h, k) B (-h, 0) C (2h, 0) D (2h, k)
Is it possible to build a triangle using the given side lengths? If so, list the angles of the triangle in order from least to greatest measure. PQ = V58, QR = 2V13, PR = 5√2
Write the conversion factor you would multiply by to change units as specified.Inches to feet
Verify the Concurrency of Altitudes of a Triangle by drawing a triangle of the given type and constructing its altitudes.Equilateral triangle
Use the information in the diagram to prove the given statement. AB= BC if and only if D, E, and B are collinear. D A E -B
Point D is the centroid of ΔABC. Use the given information to find the value of .x. BD = 4x + 5 and BF = 9x
Is it possible to build a triangle using the given side lengths? If so, list the angles of the triangle in order from least to greatest measure. ST= √29, TU = 2V17, SU = 13.9
Point D is the centroid of ΔABC. Use the given information to find the value of .x. AD = 5x and DE = 3x - 2
Use geometry drawing software to construct AB. Find the midpoint C. Draw the perpendicular bisector of AB through C. Construct a point D along the perpendicular bisector and measure DA and DB. Move D along the perpendicular bisector. What theorem does this construction demonstrate?
Use the information in the diagram to prove the given statement. PV is the perpendicular bisector of TQ for regular polygon PQRST. S W VR Q
The four towns on the map are building a common high school. They have agreed that the school should be an equal distance from each of the four towns. Is there a single point where they could agree to build the school? If so, find it. If not, explain why not. Use a diagram to explain your answer.
Write the conversion factor you would multiply by to change units as specified.Liters to kiloliters.
Point D is the centroid of ΔABC. Use the given information to find the value of .x. GD 2x 8 and GC = 3x + 3 = -
Describe the possible values of .x. K x+11, J 2x + 10 5x − 9 L
Explain why the hypotenuse of a right triangle must always be longer than either leg.
Solve the equation. Write your answer in simplest radical form. x² + 152 17² =
Verify the Concurrency of Altitudes of a Triangle by drawing a triangle of the given type and constructing its altitudes.Right scalene triangle.
What congruence postulate or theorem would you use to prove the Angle Bisector Theorem? to prove the Converse of the Angle Bisector Theorem? Use diagrams to show your reasoning.
Solve the equation. Write your answer in simplest radical form. 5² + x² = 13²
Describe the possible values of .x. 6x-11 T U 2x + 3 3x-1 V
Solve the equation. Write your answer in simplest radical form. x² + 10 = 38
Where is the circumcenter located in any right triangle? Write a coordinate proof of this result.
Suppose you are given a triangle and are asked to draw all of its perpendicular bisectors and angle bisectors. a. For what type of triangle would you need the fewest segments? What is the minimum number of segments you would need? Explain. b. For what type of triangle would you need the
The points T(2, 1), U(4, 5), and V(7, 4) are the midpoints of the sides of a triangle. Graph the three midsegments. Then show how to use your graph and the properties of midsegments to draw the original triangle. Give the coordinates of each vertex.
Write a proof of the Concurrency of Angle Bisectors of a Triangle Theorem. GIVEN AABC, AD bisects CAB, BD bisects Z CBA, DE LAB, DFL BC, DGL CA PROVE The angle bisectors intersect at D, which is equidistant from AB, BC, and CA. A G D E F B
The perimeter of ΔHGF must be between what two integers? Explain your reasoning. F 5 3 G 4 H
Ray BD bisects ∠ABC. Find the value of x. Then find m∠ABC. A B 5x D (3x + 18)° C
Ray BD bisects ∠ABC. Find the value of x. Then find m∠ABC. A D (4x + 7)° (6x - 29)° C B
You are planning a graduation party in the triangular courtyard shown. You want to fit as large a circular tent as possible on the site without extending into the walkway.a. Copy the triangle and show how to place the tent so that it just touches each edge. Then explain how you can be sure that
To complete the mobile, you need to balance the red triangle on the tip of a metal rod. Copy the triangle and decide if you should place the rod at A or B. Explain. BA MOBILE INSTRUCTIONS Step 5: Attach red triangle here.
You can estimate the width of the river at point A by taking several sightings to the tree across the river at point B. The diagram shows the results for locations C and D along the riverbank. Using ΔBCA and ΔBDA, what can you conclude about AB, the width of the river at point A? What could you
You have seen that there is a point inside any triangle that is equidistant from the three sides of the triangle. Prove that if you extend the sides of the triangle to form lines, you can find three points outside the triangle, each of which is equidistant from those three lines. X Z
Graph the lines on the same coordinate plane and find the centroid of the triangle formed by their intersections. y1=3x-4 Y2 = 3x + 5 4 3 У3 — — 2 x — 4 = - Уз
Find the area of the triangular part of the paper airplane wing that is outlined in red. Which special segment of the triangle did you use? 3 in. 9 in.
Find the length of AB and the coordinates of the midpoint of AB. A(-2, 2), B(-10, 2)
Write a coordinate proof. GIVEN AABD is a right triangle, with the right angle at vertex A. Point C is the midpoint of hypotenuse BD. PROVE Point C is the same distance from each vertex of AABD.
Find the length of AB and the coordinates of the midpoint of AB. A(-1, -3), B(7,-5)
Explain how to prove the given statement. ZQNP= ZLNM N M P
Explain how to prove the given statement. JG bisects ZFGH. F H H G
Find the coordinates of the red points in the figure if necessary. Then find OR and the coordinates of the midpoint M of RT. R(?, ?) 0(0, 0) y S(a, b) T(?, ?) X
Use geometry drawing software.a. Construct a triangle and its medians. Measure the areas of the blue, green, and red triangles. b. What do you notice about the triangles? c. If a triangle is of uniform thickness, what can you conclude about the weight of the three interior triangles? How does
To create the design below, shade the triangle formed by the three midsegments of a triangle. Then repeat the process for each unshaded triangle. Let the perimeter of the original triangle be 1.a. What is the perimeter of the triangle that is shaded in Stage 1? b. What is the total perimeter of
Explain how to prove the given statement. ΔZWX = ΔΖΥΧ W Z Y
You get off the Washington, D.C., subway system at the Smithsonian Metro station. First you visit the Museum of Natural History. Then you go to the Air and Space Museum. You record the distances you walk on your map as shown. Describe the range of possible distances you might have to walk to get
Prove the results in parts (a) - (c). GIVEN ▸ LP and MQ are medians of scalene ALMN. Point R is on LP such that LP = PR. Point S is on MQ such that MQ = QS. PROVE a. NS = NR b. NS and NR are both parallel to LM. c. R, N, and S are collinear.
In what type(s) of triangle can a vertex of the triangle be one of the points of concurrency of the triangle? Explain.
Find the coordinates of the red points in the figure if necessary. Then find OR and the coordinates of the midpoint M of RT. 0(0, 0) T(2m, 2n) R(2p, 0) X
In Exercises 46-48, write an equation of the line that passes through points A and B. A(0, 7), B(1, 10)
Find the coordinates of the red points in the figure if necessary. Then find OR and the coordinates of the midpoint M of RT. 0(0, 0) -h- R(?, ?) T h T(?, ?) X
Prove the Triangle Inequality Theorem. GIVEN > ΔΑΒC PROVE (1) AB + BC > AC (2) AC + BC> AB (3) AB + AC > BC Plan for Proof One side, say BC, is longer than or at least as long as each of the other sides. Then (1) and (2) are true. To prove (3), extend AC to D so that AB = AD and use Theorem 5.11
In Exercises 46-48, write an equation of the line that passes through points A and B. A(4, -8), B(-2,-5)
In the diagram, ΔJKL ≅ ΔRST. Find the value of x. 5x° L R 31° ト 34° S
In Exercises 44 and 45, write a coordinate proof.Any two congruent right isosceles triangles can be combined to form a single right isosceles triangle.
State which postulate or theorem you can use to prove that the triangles are congruent. Then write a congruence statement. X W Z
In Exercises 49 and 50, write the if-then form, the converse, the inverse, and the contrapositive of the given statement. A redwood is a large tree.
For what combinations of angle measures in an isosceles triangle are the congruent sides shorter than the base of the triangle? longer than the base of the triangle?
In Exercises 49 and 50, write the if-then form, the converse, the inverse, and the contrapositive of the given statement. 5x 2 18, because x = 4.
State which postulate or theorem you can use to prove that the triangles are congruent. Then write a congruence statement. P S Q R
State which postulate or theorem you can use to prove that the triangles are congruent. Then write a congruence statement. A B D C
Graph figure LMNP with vertices L(-4, 6), M(4, 8), N(2, 2), and P(-4, 0). Then draw its image after the transformation. (x, y) (x + 3, y - 4)
Graph figure LMNP with vertices L(-4, 6), M(4, 8), N(2, 2), and P(-4, 0). Then draw its image after the transformation. (x, y) → (x, y)
In the diagram, LM is the perpendicular bisector of PN.What segment lengths are equal? P 9 L 9x-3 M 4x + 1 N 6x
Graph figure LMNP with vertices L(-4, 6), M(4, 8), N(2, 2), and P(-4, 0). Then draw its image after the transformation. (x, y) → (x, y)
In the diagram, LM is the perpendicular bisector of PN.What is the value of x? P 9 L 4x + 1 N 9x-3 M 6x
In the diagram, LM is the perpendicular bisector of PN.Find MN. P 9 L 9x-3 M 4x + 1 N 6x
Describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 12 feet, 18 feet
Prove the statements in parts (a) - (c). GIVEN ▶ Plane P is a perpendicular bisector of XZ at Y. PROVE a. XW = ZW b. XV=ZV c. LVXW LVZW
Use ΔGHJ, where A, B, and C are midpoints of the sides. If AB = 3x + 8 and GJ = 2x + 24, what is AB?
Find the measure of the numbered angle. 97
In Exercises 8-10, decide whether the triangles can be proven congruent by the given postulate. AABC= AEDC by SAS -B A D C E
Tell which triangles you can show are congruent in order to prove the statement. What postulate or theorem would you use? QW = TV Q R S U W T
Describe and correct the error in writing a congruence statement for the triangles in the coordinate plane. X W 11 y 1 Y N ix AWXZ AZYX x
Use the given coordinates to determine if ∆ABC = ∆DEF. A(-2,-2), B(4, -2), C(4, 6), D(5, 7), E(5, 1), F(13, 1)
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. ΔABD, ΔCDB A B C
Find the unknown measure. R S ? T
Describe the error in the statement. A ABC A CDA by SAS. So, AB = 15 meters. x 12 m. A D 15 m C B
In Exercises 8-10, decide whether the triangles can be proven congruent by the given postulate. AFGHAJKL by ASA L F G H K
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. ΔΙΜΝ, ΔΝΟΡ M N # Q P
A base angle in an isosceles triangle measures 37°. Draw and label the triangle. What is the measure of the vertex angle?
Copy figure ABCD and draw its image after the translation. (x, y) (x + 4, y + 1)
In Exercises 8-10, decide whether the triangles can be proven congruent by the given postulate. ΔΜΝΡ = ΔΡΟM by SSS P Μ' N Q
Use the given coordinates to determine if ∆ABC = ∆DEF. A(-2, 1), B(3, -3), C(7, 5), D(3, 6), E(8, 2), F(10, 11)
Copy figure ABCD and draw its image after the translation. (x, y) (x-2, y + 3)
Use the diagram to write a plan for proof. PROVELS= LU S V H ++ U T
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. AQRV, ATSU Q R V U S T
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. ΔΥΧΖ, ΔWXZ W Z X Y
Use the diagram to write a plan for proof. PROVE ► LM = LQ N- P L -M Q
Use the given coordinates to determine if ∆ABC = ∆DEF. A(0, 0), B(6, 5), C(9, 0), D(0, -1), E(6, -6), F(9, -1)
Use coordinate notation to describe the translation. 4 units to the left, 2 units down
Use the given coordinates to determine if ∆ABC = ∆DEF. A(-5, 7), B(-5, 2), C(0, 2), D(0, 6), E(0, 1), F(4, 1)
Decide whether the figure is stable. Explain.
Which set of given information does not allow you to conclude that AD = CD? A B E D C
What is the third congruence needed to prove that ΔPQR ≅ ΔSTU using the indicated theorem?a. HL b. AAS PO R S
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. AEFH, AGHF G4 F V H E
Decide whether enough information is given to prove that the triangles are congruent using the SAS Congruence Postulate. ΔΚΕΜ, ΔΜΝΚ N K M L
Decide whether the transformation is a translation, reflection, or rotation. X
Tell whether you can use the given information to determine whether ΔABC ≅ ΔDEF. Explain your reasoning. ZA= ZD, AB = DE, AC = DF
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