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mathematics
holt mcdougal larson geometry

Questions and Answers of Holt McDougal Larson Geometry

Write a statement that is true but whose converse is false.
Sketch a line m and a point C not on line m. Make a conjecture about how many planes can be drawn so that line m and point C lie in the plane. Use postulates to justify your conjecture.
Given m∠1, find the measure of an angle that is complementary to ∠1 and the measure of an angle that is supplementary to ∠1. m/1 = 47°
Which postulate is suggested by the photo?
In Exercises 30-33, use the diagram.Name three collinear points. в C A 1D F E P
In Exercises 31-34, use the given statement to name two congruent angles. Then give a reason that justifies your conclusion. In triangle GFE, GH bisects ZEGF.
Consider the pattern 5, 5r, 5r2, 5r3,.... For what values of r will the values of the numbers in the pattern be increasing? For what values of r will the values of the numbers be decreasing? Explain.
Given m∠1, find the measure of an angle that is complementary to ∠1 and the measure of an angle that is supplementary to ∠1. m1 = 29°
Which postulate is suggested by the photo? EARTH Vuse
The distance from Springfield to Lakewood City is equal to the distance from Springfield to Bettsville. Janisburg is 50 miles farther from Springfield than Bettsville is. Moon Valley is 50 miles
Write a series of if-then statements that allow you to find the measure of each angle, given that m∠1 = 90°. Use the definition of linear pairs.
You are watching a pitcher who throws two types of pitches, a fastball (F, in white below) and a curveball (C, in red below). You notice that the order of pitches was F, C, F, F, C, C, F, F, F.
A student claims that the next number in the pattern 1, 2, 4, ... is 8, because each number shown is two times the previous number. Is there another description of the pattern that will give the same
In Exercises 31-34, use the given statement to name two congruent angles. Then give a reason that justifies your conclusion. Z1 is a supplement of 26, and 29 is a supplement of 26.
Given m∠1, find the measure of an angle that is complementary to ∠1 and the measure of an angle that is supplementary to ∠1. m/1 = 89°
Solve the equation. Write a reason for each step. 3(2x +11) 9
Copy and complete the table to show m∠2 = m∠3. E 1 F 23, H 4 G
Sketch the next figure in the pattern.
Sketch the next figure in the pattern. XX
Identify the pair(s) of congruent angles in the figures below. Explain how you know they are congruent. ZABC ZCBD A C is supplementary is supplementary B E to Z CBD. to ZDEF. F D
Use deductive reasoning to make a statement about the picture.
Identify the pair(s) of congruent angles in the figures below. Explain how you know they are congruent. N M 50° P 50° S R
Copy the logical argument. Write a reason for each step. 3x – 12 = 7x + 8 -4x 128 -4x = 20 x = -5 Given ? ? ?
How can you show that the statement, "If you play a sport, then you wear a helmet." is false? Explain.
Sketch the next figure in the pattern.
State the postulate illustrated by the diagram. If B then B
Solve the equation. Write a reason for each step. 5x – 10 = –40
Describe the pattern in the numbers. Write the next number. -6, -1, 4, 9, ...
Copy the logical argument. Write a reason for each step. 5(x1) = 4x + 13 5x 5 = 4x + 13 x 5 = 13 x = 18 Given ? ? ? 'C
Use deductive reasoning to make a statement about the picture.
Write a definition for the term collinear points, and show how the definition can be interpreted as a biconditional.
Describe the relationship between the angle measures of complementary angles, supplementary angles, vertical angles, and linear pairs.
State the postulate illustrated by the diagram. If then .C B
Which property listed is the reason for the last step in the proof? GIVEN ► m1 = 59°, m/2 = 59° PROVE m/1 = mz2 STATEMENTS 1. m/1 = 59°, m/2 = 59° 2. 59° m22 3. m/1 m/2 A Transitive Property
You can use theorems as reasons in a two-column proof. What other types of statements can you use as reasons in a two-column proof? Give examples.
Rewrite the conditional statement in if-then form.When x = 6, x2 = 36.
What is the next figure in the pattern?
Name the property of equality the statement illustrates: If XY = AB and AB = GH, then XY = GH. A Substitution B Reflexive C Symmetric D Transitive
Identify the pair(s) of congruent angles in the figures below. Explain how you know they are congruent. F G H A L 45° 44° K M W 58° Y 32° ex X Z
Make a valid conclusion in the situation. If x > 12, then -x
Make a valid conclusion in the situation.If the measure of an angle is 90°, then it is a right angle. The measure of ∠A is 90.
Use the diagram to write an example of each postulate.Postulate 6 Р H G K . q M
Rewrite the conditional statement in if-then form.The measure of a straight angle is 180°.
Describe the pattern in the numbers. Write the next number in the pattern. 1, 5, 9, 13,...
Use the property to copy and complete the statement. Reflexive Property of Congruence:_ ? = SE
Describe and correct the error in writing the if-then statement. Given statement: All high school students take four English courses. If-then statement: If a high school student takes four courses,
Postulate 8 states that through any three noncollinear points there exists exactly one plane.a. Rewrite Postulate 8 in if-then form. b. Write the converse, inverse, and contrapositive of
Use the property to copy and complete the statement. Symmetric Property of Congruence: If ??, then ZRST = /JKL.
Identify the pair(s) of congruent angles in the figures below. Explain how you know they are congruent. G L M K H
Use the diagram to write an example of each postulate.Postulate 7 P H G K .² q M
Rewrite the conditional statement in if-then form.Only people who are registered are allowed to vote.
Solve the equation. Write a reason for each step. 4х + 9 = 16 - 3x
In Exercises 5-8, write the if-then form, the converse, the inverse, and the contrapositive for the given statement.All right angles are congruent.
Describe the pattern in the numbers. Write the next number in the pattern. 3, 12, 48, 192, ...
Make a valid conclusion in the situation.If a book is a biography, then it is nonfiction. You are reading a biography.
In Exercises 5-8, write the if-then form, the converse, the inverse, and the contrapositive for the given statement.Frogs are amphibians.
Use the diagram to write an example of each postulate.Postulate 8 P H G K q M
In Exercises 7-10, write the statement that follows from the pair of statements that are given. If y> 0, then 2y> 0. If 2y> 0, then 2y - 5 # -5.
Solve the equation. Write a reason for each step. 5(3x 20) = -10
In Exercises 8-11, use the diagram at the right. 3 2
In Exercises 7-10, write the statement that follows from the pair of statements that are given.If a rectangle has four equal side lengths, then it is a square. If a polygon is a square, then it is a
For the given statement, write the if-then form, the converse, the inverse, and the contrapositive.The complementary angles add to 90°.
Describe the pattern in the numbers. Write the next number in the pattern. 10, 5, 2.5, 1.25,...
The x-axis and y-axis in a coordinate plane are perpendicular to each other. The axes form four angles. Are the four angles congruent right angles? Explain.
In Exercises 5-8, write the if-then form, the converse, the inverse, and the contrapositive for the given statement.5x + 4 = -6, because x = -2.
In Exercises 8-11, use the diagram at the right. 4 2
Name the property illustrated by the statement. If DG = CT, then CT = DG.
Name the property illustrated by the statement. ZVWX=ZVWX
Which of the following statements cannot be assumed from the diagram? P G F. H IC M в Е A
Describe the pattern in the numbers. Write the next number in the pattern. 4, 3, 1, -2, ...
For the given statement, write the if-then form, the converse, the inverse, and the contrapositive.Ants are insects.
In Exercises 7-10, write the statement that follows from the pair of statements that are given. If a = 3, then 5a = 15. If -12a = 1/2, then a = 3.
In Exercises 8-11, use the diagram at the right. 1 2 4 3
Name the property illustrated by the statement. If JK = MN and MN = XY, then JK = XY.
Solve the equation. Write a reason for each step. 2(x5) 12
In Exercises 5-8, write the if-then form, the converse, the inverse, and the contrapositive for the given statement.A regular polygon is equilateral.
In Exercises 7-10, write the statement that follows from the pair of statements that are given.If you play the clarinet, then you play a woodwind instrument. If you play a woodwind instrument, then
For the given statement, write the if-then form, the converse, the inverse, and the contrapositive.3x + 10 = 16, because x = 2.
Name the property illustrated by the statement. YZ = ZY
Describe the pattern in the numbers. Write the next number in the pattern. 1, 3'3' 0,...
In Exercises 8-11, use the diagram at the right. 4 3 2
If you decide to go to the football game, then you will miss band practice. Tonight, you are going the football game. Using the Law of Detachment, what statement can you make?
Solve the equation. Write a reason for each step. 44 2(3x + 4) = -18x
Use the diagram to write examples of the stated postulate.A line contains at least two points. R N TI Po M Q₁ X S Y
Describe the pattern in the numbers. Write the next number in the pattern. -5, -2, 4, 13,...
For the given statement, write the if-then form, the converse, the inverse, and the contrapositive.A midpoint bisects a segment.
Solve the equation. Write a reason for each step. 4(5x9) -2(x + 7) =
If two angles are vertical angles, then they have the same measure. You know that 1 and 22 are vertical angles. Using the Law of Detachment, which conclusion could you make? A mZ1>m
If Margot goes to college, then she will major in Chemistry. If Margot majors in Chemistry, then she will need to buy a lab manual. Using the Law of Syllogism, what statement can you make?
In Exercises 12 and 13, copy and complete the conjecture based on the pattern you observe in the specific cases.Given seven noncollinear points, make a conjecture about the number of ways to connect
What can you say about the sum of an even integer and an even integer? Use inductive reasoning to form a conjecture. Then use deductive reasoning to show that the conjecture is true.
Use the diagram to write examples of the stated postulate.A plane contains at least three noncollinear points. R N Ti P M Q X S Y
Decide whether the statement is true or false. If it is false, give a real-world counterexample.Through any three points, there exists exactly one line.
Decide whether the statement is true or false. If false, provide a counterexample.If a polygon has five sides, then it is a regular pentagon.
Use the diagram to determine if the statement is true or false. W Q R N J K P M X
Use the diagram to determine if the statement is true or false. W Q R Jo K NL I I P M X
Solve the equation. Write a reason for each step. 2x 15 x = 21 + 10x
Use the diagram to write examples of the stated postulate.If two planes intersect, then their intersection is a line. R N TI Po M Q₁ X S Y
In Exercises 14 and 15, sketch a diagram that represents the given information.The shape of a crystal can be represented by intersecting lines and planes. Suppose a crystal is cubic, which means it
Decide whether the statement is true or false. If false, provide a counterexample.If m∠A is 85°, then the measure of the complement of ∠A is 5°.

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