Understanding Angle Pairs in Geometry

Jul 04, 2025

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Explore the concept of angle pairs in geometry with examples of linear pairs and acute vertical angles. Learn to identify pairs of adjacent angles and opposite rays.

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Understanding Angle Pairs in Geometry

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Answer: The angle pairs that satisfy this definition are Example 5-1a Name two angles that form a linear pair. A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
Example 5-1b Name two acute vertical angles. There are four acute angles shown. There is one pair of vertical angles. Answer: The acute vertical angles are VZY and XZW.

EXAMPLE 5

Baseball. A professional baseball should weigh 5.125 ounces, with a tolerance of 0.125 ounce. Write and solve an absolute value inequality that describes the acceptable weights for a baseball. STEP 1. Write a verbal model. Then write an inequality. EXAMPLE 5.

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Example 5-1a

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Example 4-1a

Example 4-1a. Find the GCF of 16 and 24 . Method 1 List the factors. factors of 16: 1 , 2 , 4 , 8 , 16. factors of 24: 1 , 2 , 3, 4 , 6, 8 , 12, 24. Answer: The greatest common factor of 16 and 24 is 8 . Example 4-1a. Find the GCF of 16 and 24 .

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EXAMPLE 5

FINANCE. You deposit $4000 in an account that pays 2.92% annual interest. Find the balance after 1 year if the interest is compounded with the given frequency. EXAMPLE 5. Find the balance in an account. a. Quarterly. b. Daily. = 4000 1 + . 0.0292. r. 4.

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Example 7-1a

+2 +2 +2. Example 7-1a. Determine whether –15 , –13 , –11 , –9 , ... is arithmetic. Justify your answer. –15 –13 –11 –9. Answer: This is an arithmetic sequence because the difference between terms is constant. Determine whether is arithmetic. Justify your answer.

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Example 4-1a

Find the solution set for given the replacement set {(–5 , 0) , (–3 , –2) , (2 , 13) , (4 , 19)} . x. y. True or False?. –5. 0. false. –3. –2. true. 2. 13. true. 4. 19. true. Example 4-1a. Make a table. Substitute each ordered pair into the equation. Example 4-1a.

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Example 1A: Extending Geometric Sequences

Example 1A: Extending Geometric Sequences . Find the next three terms in the geometric sequence. 1, 4, 16, 64,…. Step 1 Find the value of r by dividing each term by the one before it. 1 4 16 64. The value of r is 4.  4  4  4.

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Check It Out! Example 1a

Check It Out! Example 1a. Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. cos A. Check It Out! Example 1b. Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. tan B. Check It Out! Example 1c.

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Example 1A:

Example 1A:. Compare m  BAC and m  DAC. Compare the side lengths in ∆ ABC and ∆ ADC. AB = AD AC = AC BC > DC. By the Converse of the Hinge Theorem, m  BAC > m DAC. Example 1B:. Compare EF and FG. Compare the sides and angles in ∆ EFH angles in ∆ GFH.

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EXAMPLE 5

In the diagram, ∆ TPR ~ ∆ XPZ . Find the length of the altitude PS. TR. 12. 3. XZ. 16. 4. 6 + 6. =. =. =. 8 + 8. EXAMPLE 5. Use a scale factor. SOLUTION. First, find the scale factor of ∆ TPR to ∆ XPZ. =. 3. PS. 3. 4. 4. PY. PS. =. 20. =. PS. 15.

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Example 1A: Classifying Three-Dimensional Figures

Three-dimensional figures, or solids, can be made up of flat or curved surfaces. Each flat surface is called a face . An edge is the segment that is the intersection of two faces. A vertex is the point that is the intersection of three or more faces.

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Example 7-1a

Let A , B , C , and D be vertices of a rectangle with sides a units long, and sides b units long. Place the square with vertex A at the origin, along the positive x -axis, and along the y -axis. Label the vertices A , B , C , and D. Example 7-1a.

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EXAMPLE 5

a. PQRS is inscribed in a circle, so opposite angles are supplementary. a. m Q + m S = 180 o. m P + m R = 180 o. EXAMPLE 5. Use Theorem 10.10. Find the value of each variable. SOLUTION. 75 o + y o = 180 o. 80 o + x o = 180 o. y = 105. x = 100. b.

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EXAMPLE 5

You work 4 hours and earn $36 . What is your earning rate?. You travel for 2.5 hours at 50 miles per hour. How far do you go?. 36 dollars. 4 hours. 50 miles. (2.5 hours ). 1 hour. EXAMPLE 5. Use unit analysis with operations. SOLUTION. = 9 dollars per hour. SOLUTION.

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EXAMPLE 5

Standardized Test Practice. EXAMPLE 5. SOLUTION. The lateral surface area of a cylinder is equal to the area of its curved surface. This surface becomes a rectangle in the net of the cylinder, with length equal to the circumference of the base. ANSWER.

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Example 4-1a

In and Find SU. S. From the Triangle Proportionality Theorem,. Example 4-1a. In and Find BY. B. Example 4-1c. Answer: 15.75.

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Example 7-1a

Write in radical form. Definition of. Answer:. Example 7-1a. Write in radical form. Definition of. Answer:. Example 7-1b. Write each expression in radical form. a. b. Answer:. Answer:. Example 7-1c. Write using rational exponents. Answer:. Definition of. Example 7-2a.

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Example 1A:

A diagonal of a square divides it into two congruent isosceles right triangles. Since the base angles of an isosceles triangle are congruent, the measure of each acute angle is 45°. So another name for an isosceles right triangle is a 45°-45°-90° triangle.

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Example 1a

A. Name a plane that is parallel to plane RST. A. plane WTZ B. plane SYZ C. plane WXY D. plane QRX. Example 1a. Choose the segment skew to MP. ___. A. PM B. TS C. PO D. MQ. ___. ___. ___. 5-Minute Check 2. A. 0 B. undefined C. 3 D. D. Find the slope of the line.

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Example 7-1a

Example 7-1a. Determine whether the graph shows a positive correlation , a negative correlation , no correlation . If there is a positive or negative correlation, describe it. The graph shows average personal income for U.S. citizens.

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Example 8-1a

Solve. Original equation. Add 1 to each side to isolate the radical. Square each side to eliminate the radical. Find the squares. Add 2 to each side. Example 8-1a. Original equation. Replace y with 38. Simplify. Example 8-1b. Check.

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OP-1A – Power Point Presentation Example

OP-1A – Power Point Presentation Example. Coke is it!. Craig Bench: Example of a Company Presentation. Coke is it!. Coca-Cola is the world’s top soft drink producer

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