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mathematics
holt mcdougal larson geometry

Questions and Answers of Holt McDougal Larson Geometry

Find the unknown side length of the right triangle using the Pythagorean Theorem or a Pythagorean triple. X 60 68
In Exercises 9-14, determine whether the triangles are similar. If they are, write a similarity statement. A 65° B 65° C D E
Show that the triangles are similar and write a similarity statement. Explain your reasoning. A B 27 21 14 E C 18 D
In Exercises 9-14, determine whether the triangles are similar. If they are, write a similarity statement. R. 35° 85° Q S T 65% 35° U
Use the diagram and the given information to find the unknown length. Given A CB DE BA EF B 6 C. find BA. D 4 E 7 F
Show that the triangles are similar and write a similarity statement. Explain your reasoning. 15 H F 5 G 18 16.5 24 J 5.5 K
Find the value of the variable. 3 4.5 Z 1.5
In Exercises 9-14, determine whether the triangles are similar. If they are, write a similarity statement. M X 45% 45° N Z
In the diagram, JKLM ~ EFGH.Find the perimeter of each polygon. H 3 G 11 zº E 8 F 20 65° K X 30 M L
In the diagram, JKLM ~ EFGH.Find the values of x, y, and z. H 3 G 11 zº E 8 F 20 65° K X 30 M L
In Exercises 9-14, determine whether the triangles are similar. If they are, write a similarity statement. G 48° 14 H J 42° L
Find the value of the variable. 8 4 y 6
Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of Triangle B to Triangle A. R A 18 112% 8 T S 10, K L 112° 24 B
In the diagram, JKLM ~ EFGH.Find the scale factor of JKLM to EFGH. H 3 G 11 zº E 8 F 20 65° K X 30 M L
Use the diagram to complete the statement. X = ?
For the figure at the right, which statement is not necessarily true? P U Q T R S
Find the value of the variable. 15 21 X 14
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor. C 10 12 D 5 E 4 9.6 8 T
Determine whether the two triangles are similar. If they are similar, write a similarity statement and find the scale factor of Triangle B to Triangle A. D 9 E A 15 F B X 10 Y 6 W
Use the diagram to complete the statement. y= y = ?
Use the given information to determine whether KM ∣∣ JN. Explain your reasoning.. J 22.5 K 25 L 20 N 18 M
Determine whether the polygons are similar. If they are, write a similarity statement and find the scale factor. R 48 U 64 64 S 48 T Z 24 W 32 32 Y 24 X
Use the diagram to complete the statement. ? 25 ? 18 의
Triangles ABC and DEF are similar. Which statement is not correct? (A) BC AC EF DF B) AB CA DE FD = I BC FD EF AB BC EF DE
Use the given information to determine whether KM ∣∣ JN. Explain your reasoning.. L 18 K 24 10 J M 15 N
Use the diagram to complete the statement. 25 ? ? 12
Is either ΔJKL or ΔRST similar to ΔABC? A 16 B 14 7 17.5 20 С К 25 20 16 T 10.5 JR 12 S
Is either ΔJKL or ΔRST similar to ΔABC? A B 7 8 C PR 6 12 K 7 11 3.5 R S 4 6 T
Use the diagram to complete the statement. BA ? ? AC СВ ?
Verify that ΔABC ~ ΔDEF. Find the scale factor of ΔABC to ΔDEF. AABC: AB = 10, BC = 16, CA = 20 ADEF: DE = 25, EF = 40, FD = 50
Use the given information to determine whether KM ∣∣ JN. Explain your reasoning. K 5 8, 12 M 7.5 N
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. DEFG PQRS E D G F R Q S P
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. L HJKL ~ WXYZ H K W Z
Use the diagram to complete the statement. ΔΑΒC~ ?
Verify that ΔABC ~ ΔDEF. Find the scale factor of ΔABC to ΔDEF. A ABC: BC = 18, AB = 15, AC = 12 A DEF: EF = 12, DE = 10, DF = 8
List all pairs of congruent angles for the figures. Then write the ratios of the corresponding sides in a statement of proportionality. ΔΑΒC ~ ΔΙΜΝ A L C B N M
In Exercises 46-48, write an equation of the line that passes through points A and B. A(5,-21), B(0, 4)
Can you assume that corresponding sides and corresponding angles of any two similar triangles are congruent? Explain.
Write three ratios that are equivalent to the ratio 3:4. Explain how you found the ratios.
Describe the translation in words and write the coordinate rule for the translation. 3- y X
Use the given information to draw a sketch. Then write a proof. GIVEN ASTU~APQR PROVE Point V lies on TU so that SV bisects ZTSU. Point N lies on QR so that PN bisects ZQPR. SV_ST PN PQ
If you know two triangles are similar by the SAS Similarity Theorem, what additional piece(s) of information would you need to know to show that the triangles are congruent?
Given that ΔABC is a right triangle and D, E, and Fare midpoints, prove that m∠DEF = 90°. B D A E F C
Suppose the scale of a model of the Eiffel Tower is 1 inch: 20 feet. Explain how to determine how many times taller the actual tower is than the model.
Describe the translation in words and write the coordinate rule for the translation. 3 y 2 X
Write a paragraph proof of the SAS Similarity Theorem. AB DE PROVE AABC~ ADEF GIVENZA = ZD, AC DF G A B H C D F
If two polygons are congruent, must they be similar? If two polygons are similar, must they be congruent? Explain.
A portion of a water slide in an amusement park is shown. Find the length of EF. 40 ft D E F B 25 ft C
Copy and complete: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are _?_.
Copy and complete: A __?__ is a drawing that has the same shape as the object it represents.
Copy and complete: Two polygons are similar if corresponding angles are __?__ and corresponding side lengths are_?_.
Explain how you could use similar triangles to show that any two points on a line can be used to calculate its slope. X
In Exercises 41-44, use the diagram.Name three pairs of corresponding angles. 2 34 5 6 78
In Exercises 41-44, use the diagram. Find m/1 + m27.
In Exercises 41-44, use the diagram.Name two pairs of alternate interior angles. 2 34 56 7 8
State the postulate or theorem you would use to prove the triangles congruent. Then write a congruence statement. Q R T S
Prove that if an acute angle in one right triangle is congruent to an acute angle in another right triangle, then the triangles are similar.
In Exercises 41-44, use the diagram.Name two pairs of alternate exterior angles. 12 34 5 6 78
Perform the following operations. Then simplify. از 4 3 لا
Ruby is standing in her back yard and she decides to estimate the height of a tree. She stands so that the tip of her shadow coincides with the tip of the tree's shadow, as shown. Ruby is 66 inches
You can measure the width of the lake using a surveying technique, as shown in the diagram. a. What postulate or theorem can you use to show that the triangles are similar? b. Find the width of the
Describe the translation in words and write the coordinate rule for the translation. y X
Certain sections of stained glass are sold in triangular beveled pieces. Which of the three beveled pieces, if any, are similar? 3 in. 5 in. 3 in. 4 in. 7 in. 4 in. 5.25 in. 3 in. 3 in.
Perform the following operations. Then simplify. 5 N 2
Perform the following operations. Then simplify. (-3) 72
In Exercises 26-29, is it possible for ΔJKL and ΔXYZ to be similar? Explain why or why not. mLJ + mLK = 85° and mLY + mLZ= 80°
Explain why all equilateral triangles are similar. Include sketches in your answer.
In perspective drawing, lines that are parallel in real life must meet at a vanishing point on the horizon. To make the train cars in the drawing appear equal in length, they are drawn so that the
Suppose you are given two right triangles with one pair of corresponding legs and the pair of corresponding hypotenuses having the same length ratios.a. The lengths of the given pair of corresponding
An air hockey player returns the puck to his opponent by bouncing the puck off the wall of the table as shown. From physics, the angles that the path of the puck makes with the wall are congruent.
Perform the following operations. Then simplify. 3 2
In Exercises 26-29, is it possible for ΔJKL and ΔXYZ to be similar? Explain why or why not. AJKL is a right triangle and mLX+ m2Y = 150°.
Which postulate or theorem could you use to show that the three triangles that make up the racecar window net are similar? Explain. U A B BG CF, CF DE G E
Find coordinates for point E so that ΔABC ~ ΔADE. A(0, 0), B(0, 6), C(3, 0), D(0, 9), E(x, y)
In Exercises 26-29, is it possible for ΔJKL and ΔXYZ to be similar? Explain why or why not. mLJ= 87° and m2 Y = 94°
In Exercises 26-29, is it possible for ΔJKL and ΔXYZ to be similar? Explain why or why not. mLJ = 71°, mLK = 52°, mLX = 71°, and mLZ = 57°
In Exercises 18-23, use the diagram to copy and complete the statements. mLQPN = ?
In the diagram, AB: BC is 2:7 and AC = 36. Find AB and BC. А B -36- C
The real estate term lake frontage refers to the distance along the edge of a piece of property that touches a lake.a. Find the lake frontage (to the nearest tenth of a yard) for each lot shown. b.
In Exercises 18-23, use the diagram to copy and complete the statements. mLPNQ = ?
In the figure at the right, find the length of BD. D A 5 E 3 C -B
The black triangles are similar. Identify the type of special segment shown in blue, and find the value of the variable. 16 18 27 X
In Exercises 18-23, use the diagram to copy and complete the statements. RN = ?
The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles of the triangle. 3:5:10
The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles of the triangle. 2:7:9
The black triangles are similar. Identify the type of special segment shown in blue, and find the value of the variable. ~y-1 18 16 11
On the map below, Idaho Avenue bisects the angle between University Avenue and Walter Street. To the nearest yard, what is the distance along University Avenue from 12th Street to Washington Street?
In Exercises 18 and 19, make a sketch that can be used to show that the statement is false.If the ratios of two pairs of sides of two triangles are proportional, then the triangles are similar.
In Exercises 18-23, use the diagram to copy and complete the statements. PQ = ?
Find coordinates for point E so that ΔABC ~ ΔADE. A(0, 0), B(0, 3), C(4, 0), D(0, 7), E(x, y)
Find coordinates for point E so that ΔABC ~ ΔADE. A(0, 0), B(0, 1), C(6, 0), D(0, 4), E(x, y)
The measures of the angles of a triangle are in the extended ratio given. Find the measures of the angles of the triangle. 11:12:13
Prove the Triangle Proportionality Theorem. GIVEN QS TU QT SU TR UR PROVE ▶ - S R
In Exercises 18-23, use the diagram to copy and complete the statements. NM = ?
In Exercises 18-23, use the diagram to copy and complete the statements. mLNQP = ?
A student claims that AB = AC using the method shown. Describe and correct the student's error. By Theorem 6.7, BD = AB Because CD AC BD CD, it follows that AB = AC. A- B D x C
Triangles NPQ and RST are similar. The side lengths of ΔNPQ are 6 inches, 8 inches, and 10 inches, and the length of an altitude is 4.8 inches. The shortest side of ΔRST is 8 inches long.Find the
Use the number line to find the ratio of the distances. A 01 B 842 +3 C44 31 3 4 5 46 9 D 7 48 8 6 E + 10 11 12 F + + 13 14 15 16
Sketch the triangles using the given description. Explain whether the two triangles can be similar. The side lengths of AABC are 24, 8x, and 54, and the side lengths of ADEF are 15, 25, and 7x.
Use the diagram to find the value of each variable. 6 9 d 6 3 C a b 5 6 4.5 7.5

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