P Preliminary Concepts 1 Line And Angle Relationships 2 Parallel Lines 3 Triangles 4 Quadrilaterals 5 Similar Triangles 6 Circles 7 Locus And Concurrence 8 Areas Of Polygons And Circles 9 Surfaces And Solids 10 Analytic Geometry 11 Introduction To Trigonometry A Appendix Chapter1: Line And Angle Relationships
1.1 Early Definitions And Postulates 1.2 Angles And Their Relationships 1.3 Introduction To Geometric Proof 1.4 Relationships: Perpendicular Lines 1.5 The Format Proof Of A Theorem 1.CR Review Exercises 1.CT Test Section1.2: Angles And Their Relationships
Problem 1E: What type of angle has the given measure? a 47 b 90 c 137.3 Problem 2E: What type of angle has the given measure? a 115 b 180 c 30 Problem 3E: What relationship, if any, exists between two angles a with measures of 37 and 53? b with measures... Problem 4E: What relationship, if any, exists between two angles a with equal measures? b that have the same... Problem 5E: In Exercises 5 to 8, describe in one word the relationship between the angles. ABD and DBC Problem 6E: In Exercises 5 to 8, describe in one word the relationship between the angles. 7 and 8 Problem 7E: In Exercises 5 to 8, describe in one word the relationship between the angles. 1 and 2 Problem 8E: In Exercises 5 to 8, describe in one word the relationship between the angles. 3 and 4 Problem 9E: Use drawings as needed to answer each of the following questions. Must two rays with a common... Problem 10E: Suppose that AB,AC,AD,AE, and AF are coplanar, Exercises 10-13 Classify the following as true or... Problem 11E: Exercises 10-13 Without using a protractor, name the type of angle represented by: a BAE b FAD c BAC... Problem 12E: Exercises 10-13 What, if anything, is wrong with the claim mFAB+mBAE=mFAE Problem 13E: Exercises 10-13 FAC and CAD are adjacent and AF and AD are opposite rays. What can you conclude... Problem 14E: For Exercises 14 and 15, let m1=x and m2=y. Using variables x and y, write an equation that... Problem 15E: For Exercises 14 and 15, let m1=x and m2=y. Using variables x and y, write an equation that... Problem 16E: Given: mRST=39 mTSV=23 Find: mRSV Exercises 1624 Problem 17E: Exercises 1624 Given: mRSV=59 mTSV=17 Find: mRST Problem 18E: Exercises 1624 Given: mRST=2x+9 mTSV=3x2 mRSV=67 Find: x Problem 19E: Exercises 1624 Given: mRST=2x10 mTSV=x+6 mRSV=4(x6) Find: xandmRSV Problem 20E: Exercises 1624 Given: mRST=5(x+1)3 mTSV=4(x2)+3 mRSV=4(2x+3)7 Find: xandmRSV Problem 21E: Exercises 1624 Given: mRST=x2 mTSV=x4 mRSV=45 Find: xandmRST Problem 22E: Exercises 1624 Given: mRST=2x3 mTSV=x2 mRSV=49 Find: xandmTSV Problem 23E: Exercises 1624 Given: STbisectsRSV mRST=x+y mTSV=2x2y mRSV=64 Find: xandy Problem 24E: Exercises 1624 Given: STbisectsRSV mRST=2x+3y mTSV=3xy+2 mRSV=80 Find: xandy Problem 25E: Given: AB and AC in plane P as shown AD intersects P at points A CABDAC DACDAB What can you... Problem 26E: Two angles are complementary. One angle is 12 larger than the other. Using two variable x and y,... Problem 27E: Two angles are supplementary. One angle is 24 more than twice the other. Using two variable x and y,... Problem 28E: For two complementary angles, find an expression for the measure of the second angle if the measure... Problem 29E: Suppose that the two angles are supplementary. Find expressions for the supplements, using the... Problem 30E: On the protractor shown, NP bisects MNQ. Find x. Exercises 30,31 Problem 31E: Exercises 30,31 On the protractor shown for Exercise 30, MNP and PNQ are complementary. Find x. Problem 32E: Classify as true or false: a If points P and Q lie in the interior of ABC, then PQ lies in the... Problem 33E Problem 34E Problem 35E: In Exercises 33 to 40, use only a compass and a straightedge to perform the indicated constructions.... Problem 36E Problem 37E: Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On... Problem 38E Problem 39E Problem 40E Problem 41E: Given: 1 and 2 as shown in, sketch the bisectors of 1 and 2. What is the measure of the angle formed... Problem 42E Problem 43E Problem 44E: If mTSV=38,mUSW=40, and mTSW=61, find mUSV. Exercises 44, 45 Problem 45E: Exercises 44, 45 If mTSU=x+2z,mUSV=xz, and mVSW=2xz, find x if mTSW=60. Also, find z if mUSW=3x6. Problem 46E Problem 47E: On the hanging sign, the three angles (ABD,ABC,andDBC) at vertex B have the sum of measures 360. If... Problem 48E: With 0x90, an acute angle has a measure x. Find the difference between the measure of its supplement... Problem 37E: Draw a triangle with three acute angles. Construct angle bisectors for each of the three angles. On...
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Answer the question
( it’s not the first option Corresponding Angles Postulate)
Transcribed Image Text: **Diagram Explanation:**
The diagram shows angles \( \angle X \), \( \angle Y \), and \( \angle Z \) formed by lines \( m \) and \( n \) intersected by a transversal.
**Proof:**
Given: \( \angle X \cong \angle Y \)
**To Prove:** \( m \parallel n \)
**Statements and Reasons:**
1. \( \angle X \cong \angle Y \)
- **Reason:** Given
2. \( \angle Y \cong \angle Z \)
- **Reason:** Vertical angle theorem
3. \( \angle X \cong \angle Z \)
- **Reason:** Transitive property of congruence
4. \( m \parallel n \)
- **Reason:** ____________________________
**Question:**
Which reason completes the proof?
- \( A \) Corresponding Angles Postulate
- \( B \) Alternate Exterior Angles Theorem
- \( C \) Converse of the Corresponding Angles Postulate
- \( D \) Converse of the Alternate Exterior Angles Theorem
The correct answer to complete the proof is option \( C \), the **Converse of the Corresponding Angles Postulate**, which allows us to conclude that the lines \( m \) and \( n \) are parallel given that the corresponding angles are congruent.
Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.
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