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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
Can you use the given information to determine that AB ≅ BC? Justify your answer. BD bisects AC, AD 1 BD A B D C
State the segment or triangle that represents the image. You can use tracing paper to help you see the rotation. 180° rotation of ATUA about E
In Exercises 35 and 36, write a proof. GIVEN PQ bisects /SPT, SP = TP PROVE · ASPQ = ATPQ P S Q
Suppose you have two sailboats. What information do you need to know to prove that the triangular sails are congruent using SAS? using HL?
In Exercises 32-37, find the values of x and y. xº 47° y 15°
In Exercises 35 and 36, write a proof. GIVEN PROVE VX = XY, XW YZ, XW|| YZ = • AVXW = AXYZ Z -W
Use the x- and y-intercepts to write an equation of the line. 40+ y 20 X
Find the value of x that makes m ∣∣ n. 51° F of AE AC m
In Exercises 32-37, find the values of x and y. 35° 18° yᵒ ро
Use the given information and the diagram to write a proof. GIVEN MN = KN, LPMN = ZNKL PROVE ► 21 = 42 P M N K Q L
Solve for the variables in the transformation of AB to CD and then to EF. A(2, 3), B(4, 2a) Translation: (x, y) → (x-2, y + 1) C(m 3, 4), D(n - 9,5) Reflection: in x-axis E(0, g- 6), F(8h, -5)
Use the given information and the diagram to write a proof. GIVEN TS TV, SR= VW PROVE Z1 = 42 R S X 2 W
Find the value of x that makes m ∣∣ n. 42° 2x° m n
The measure of an exterior angle of an isosceles triangle is 130°. What are the possible angle measures of the triangle? Explain.
The dimensions of a sports pennant are given in the diagram. Find the values of x and y. 791 STATES
The design for a kite shows the layout and dimensions for only half of the kite.a. What type of transformation can a designer use to create plans for the entire kite? b. What is the maximum width of the entire kite? 2 ft
Which triangle congruence can you prove, then use to prove that ∠FED ≅ ∠ABF? C A 70° 70° D 40° 卅 E B
Find the value of x that makes m ∣∣ n. 101° (x + 16)° 3V n
Use the given information and the diagram to write a proof. GIVEN BA= BC, D and E are midpoints, ZA= ZC, DF = EF PROVE FG = FH A D G B H E C
How many lines can be drawn that fit each description? Copy the diagram and sketch all the lines. Line(s) through B and parallel to AC
Write a two-column proof. GIVEN CR= CS, QC L CR, QC L CS PROVE AQCR= AQCS S Q C P R
In Exercises 37 and 38, write a proof. GIVEN PROVE A D is the midpoint of AC. · AABD = ACBD B D C
To make a zig-zag pattern, a graphic designer sketches two parallel line segments. Then the designer draws blue and green triangles as shown below. A B C D K E F G
Three people are standing on a stage. The distances between the three people are shown in the diagram. Classify the triangle formed by its sides. Then copy the triangle, measure the angles, and classify the triangle by its angles. 6.5 ft 8 ft 5 ft
Write an equation of a line that passes through (-3, -1) and is parallel to y = 3x + 2.
You are stenciling a room in your home. You want to use the stencil pattern below on the left to create the design shown. Give the angles and directions of rotation you will use to move the stencil from A to B and from A to C. A C B D
Some words reflect onto themselves through a vertical line of reflection. An example is shown.a. Find two other words with vertical lines of reflection. Draw the line of reflection for each word. b. Find two words with horizontal lines of reflection. Draw the line of reflection for each word. WOW
The measure of an exterior angle of an isosceles triangle is x°. What are the possible angle measures of the triangle in terms of x? Describe all the possible values of x.
The Transamerica Pyramid building shown in the photograph has four faces shaped like isosceles triangles. The measure of a base angle of one of these triangles is about 85°. What is the approximate measure of the vertex angle of the triangle? 85°
How many lines can be drawn that fit each description? Copy the diagram and sketch all the lines. Line(s) through A and perpendicular
In chess, six different kinds of pieces are moved according to individual rules. The Knight (shaped like a horse) moves in an "L" shape. It moves two squares horizontally or vertically and then one additional square perpendicular to its original direction.a. Describe the translation used by the
You are making a kaleidoscope. The directions state that you are to arrange three pieces of reflective mylar in an equilateral and equiangular triangle. You must cut three strips from a piece of mylar 6 inches wide. What are the side lengths of the triangle used to form the kaleidoscope? What are
Is there an angle measure that is so small that any triangle with that angle measure will be an obtuse triangle? Explain.
Decide which method, SSS, SAS, or HL, can be used to prove that the triangles are congruent. ΔΗ]Κ = ΔΙΚΙ Η + # K
In the pattern below, each small triangle is an equilateral triangle with an area of 1 square unit.a. Reasoning Explain how you know that any triangle made out of equilateral triangles will be an equilateral triangle. b. Area Find the areas of the first four triangles in the pattern. c. Make a
How many lines can be drawn that fit each description? Copy the diagram and sketch all the lines. Line(s) through D and C
Decide which method, SSS, SAS, or HL, can be used to prove that the triangles are congruent. AUTV = AWVT T W
The brace of a sling chair forms a triangle with the seat and legs of the chair. Suppose m∠2 = 50° and m∠3 = 65°. 6 3 2 4 1 5
A piece of paper is folded in half and some cuts are made, as shown. Which figure represents the unfolded piece of paper? 고
Show that ΔABC and ΔDEF are right triangles and use the HL Congruence Theorem to verify that ΔDEF is a congruence transformation of ΔABC. D F E 1 AY 1 A C B X
The brace of a sling chair forms a triangle with the seat and legs of the chair. Suppose m∠2 = 50° and m∠3 = 65°. 9 Ge 3 1 2 டீ சு
The variable expressions represent the angle measures of a triangle. Find the measure of each angle. Then classify the triangle by its angles. MLA = x° mLB = (4x)° mLC = (5x)°
Decide which method, SSS, SAS, or HL, can be used to prove that the triangles are congruent. AXYZ ARQZ X Z R Q
Which inequality describes the possible measures of an angle of a triangle? A 0° ≤ x ≤ 180° B 0°
Simplify the expression. Variables a and b are positive. -a-0 0 − (−b)
The brace of a sling chair forms a triangle with the seat and legs of the chair. Suppose m∠2 = 50° and m∠3 = 65°. 6 3 2 4 1 5
The brace of a sling chair forms a triangle with the seat and legs of the chair. Suppose m∠2 = 50° and m∠3 = 65°. 6 3 11 2 4 5
Simplify the expression. Variables a and b are positive. |(a + b) - al
The variable expressions represent the angle measures of a triangle. Find the measure of each angle. Then classify the triangle by its angles. mLA = x° mLB = (5x)° mLC = (x + 19)°
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The first bend is made 6 inches from one end. Describe two ways you could complete the triangle.
The variable expressions represent the angle measures of a triangle. Find the measure of each angle. Then classify the triangle by its angles. mLA = (x 22)° - mLB= (x + 16)° mLC = (2x 14)°
Simplify the expression. Variables a and b are positive. 2a + 2b 2
Use the information in the diagram to answer the question. Explain your reasoning. Is p | q? 45° 130% 1 2 q
Simplify the expression. Variables a and b are positive. √(2a)²
Use the information in the diagram to answer the question. Explain your reasoning. Is A ABC isosceles? 130% B 50% A C
Simplify the expression. Variables a and b are positive. V(2aa)² + (0- b)²
Simplify the expression. Variables a and b are positive. √(-b)²
Use the information in the diagram to answer the question. Explain your reasoning.Write a proof. GIVEN AABC is equilateral, 2 CAD LABE = ZBCF. PROVE A DEF is equilateral. B E A LL F C
The figure below shows an initial plan for a triangular flower bed that Mary and Tom plan to build along a fence. They are discussing what the measure of ∠1 should be.Did Mary and Tom both reason correctly? If not, who made a mistake and what mistake was made? If they did both reason correctly,
What quadrant contains the point? (-2,4)
Copy and complete the given function table. ? ? -2 -6 0 0 1 3
What quadrant contains the point? (-1, -3)
Each figure is a regular polygon. Find the value of x. 12x - 10 4x + 6
What quadrant contains the point? (5,-2)
Copy and complete the given function table. X y=x-4 -7 ? 0 ? 5 ?
Use the Distance Formula to decide whether AB ≅ AC. A(0, 0), B(-5, -6), C(6, 5)
Use the Distance Formula to decide whether AB ≅ AC. A(3, 3), B(0, 1), C(-1,0)
Each figure is a regular polygon. Find the value of x. x + 2 2x-5
Each figure is a regular polygon. Find the value of x. 3x + 7 6x + 1
Use the Distance Formula to decide whether AB ≅ AC. A(0, 1), B(4, 7), C(-6, 3)
Use the Distance Formula to decide whether AB ≅ AC. A(-3,0), B(2, 2), C(2,-2)
Copy the triangle and measure its angles. Classify the triangle by its sides and by its angles. X₁ Z
Copy the triangle and measure its angles. Classify the triangle by its sides and by its angles. L M N
Match the triangle description with the most specific name.Angle measures: 30°, 60°, 90°A. Isosceles B. Scalene C. Right D. Obtuse E. Equilateral F. Equiangular
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A(3, 3), B(6, 9), C(6, -3)
Copy the triangle and measure its angles. Classify the triangle by its sides and by its angles. K H
Write a congruence statement for any figures that can be proved congruent. Explain your reasoning. W Z
Match the triangle description with the most specific name.Side lengths: 2 cm, 2 cm, 2 cmA. Isosceles B. Scalene C. Right D. Obtuse E. Equilateral F. Equiangular
Match the triangle description with the most specific name.Angle measures: 60°, 60°, 60°A. Isosceles B. Scalene C. Right D. Obtuse E. Equilateral F. Equiangular
Match the triangle description with the most specific name.Side lengths: 6 m, 3 m, 6 mA. Isosceles B. Scalene C. Right D. Obtuse E. Equilateral F. Equiangular
Match the triangle description with the most specific name.Side lengths: 5 ft, 7 ft, 9 ftA. Isosceles B. Scalene C. Right D. Obtuse E. Equilateral F. Equiangular
Match the triangle description with the most specific name.Angle measures: 20°, 125°, 35°A. Isosceles B. Scalene C. Right D. Obtuse E. Equilateral F. Equiangular
Can a right triangle also be obtuse? Explain why or why not.
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle.
Write a congruence statement for any figures that can be proved congruent. Explain your reasoning. A B C D E
Find the value of x. Then classify the triangle by its angles. 60° 60° 아
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle. A(1, 9), B(4, 8), C(2, 5)
Write a congruence statement for any figures that can be proved congruent. Explain your reasoning. A 丰 F E G 丰 D
Find the measure of the numbered angle. 17
Find the measure of the exterior angle shown. xº (2x - 2)° 45°
Find the measure of the numbered angle. 42
Write a congruence statement for any figures that can be proved congruent. Explain your reasoning. X Y N M
Find the measure of the exterior angle shown. (3x+6) 24° (2x + 18)°
Explain how to use the Corollary to the Triangle Sum Theorem to find the measure of each angle. 3x⁰ 2x°
Find the value of x. Then classify the triangle by its angles. to 3x 60°
Find the value of x. Then classify the triangle by its angles. 64° 70° 如
Find the measure of the numbered angle. 43
Find the measure of the exterior angle shown. (3x + 2)° xº 1
A hexagon is contained in a cube, as shown. Each vertex of the hexagon lies on the midpoint of an edge of the cube. This hexagon is equiangular. Explain why it is also regular. A
The rug design is made of congruent triangles. One triangular shape is used to make all of the triangles in the design. Which property guarantees that all the triangles are congruent?
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