Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

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Geometry 2.7 Geometry 2.7 Big Idea: Prove Big Idea: Prove Angle Pair Angle Pair Relationships Relationships

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Theorem 2.4: Congruent Supplements Theorem If two angles are supplementary to the same angle (or to congruent angles),then they are congruent.

Transcript of Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Page 1: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Geometry 2.7Geometry 2.7 Big Idea: Prove Big Idea: Prove

Angle PairAngle PairRelationshipsRelationships

Page 2: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Theorem 2.3:Theorem 2.3:Right Angles Right Angles Congruence TheoremCongruence Theorem

All right angles are All right angles are congruent.congruent.

Page 3: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Theorem 2.4:Theorem 2.4:Congruent Supplements Congruent Supplements TheoremTheorem

If two angles are If two angles are supplementary to the supplementary to the same angle (or to same angle (or to congruent angles),then congruent angles),then they are congruent.they are congruent.

Page 4: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

ExampleExample

If angles 1 and 3 are supplementary and If angles 1 and 3 are supplementary and angles 5 and 3 are supplementary, angles 5 and 3 are supplementary, then angles 1 and 5 are congruent.then angles 1 and 5 are congruent.

Page 5: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Theorem 2.5:Theorem 2.5:Congruent Complements Congruent Complements TheoremTheorem

If two angles are If two angles are complementary to the complementary to the same angle (or to same angle (or to congruent angles),then congruent angles),then they are congruent.they are congruent.

Page 6: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

ExampleExample11 2 32 3

If angles 1 and 2 are If angles 1 and 2 are complementary and angles 1 complementary and angles 1 and 3 are complementary, then and 3 are complementary, then angles 2 and 3 are congruent.angles 2 and 3 are congruent.

Page 7: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Theorem 2.6:Theorem 2.6:Vertical Angles Vertical Angles Congruence TheoremCongruence Theorem

Vertical angles are Vertical angles are congruent.congruent.

Page 8: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

ExampleExample

4 24 2 1 3 1 3

Page 9: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Postulate 12:Postulate 12:Linear Pair PostulateLinear Pair PostulateIf two angles form a linear If two angles form a linear

pair, then they are pair, then they are supplementary.supplementary.

Page 10: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

ExampleExample

Since angles 1 and 2 form a Since angles 1 and 2 form a linear pair, they must be linear pair, they must be supplementary and supplementary and m m 1 + 1 + mm 2 = 180 2 = 180ºº

Page 11: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

Proof 1: Right Angles Proof 1: Right Angles Congruence TheoremCongruence Theorem

Given: PQR and UTS are right Given: PQR and UTS are right anglesangles

Prove: PQR UTSProve: PQR UTS

Page 12: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

StatementStatement ReasonReason1. 1. 1.1.2. 2. mm PQR = 90 PQR = 90º;º; 2. 2. m m UTS = 90º UTS = 90º3.3.m m PQR = PQR = mm UTS UTS 3. 3. 4.4. 4.4.5.5. 5. 5.

Given: PQR and UTS are right anglesProve: PQR UTS

Page 13: Geometry 2.7 Big Idea: Prove Angle Pair Big Idea: Prove Angle PairRelationships.

ExampleExample

If If mm 1 = 112 1 = 112º, find the º, find the measure of angles 2, 3 & 4.measure of angles 2, 3 & 4.


1.3 a: Angles, Rays, Angle Addition, Angle Relationships G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent;

1.3 a: Angles, Rays, Angle Addition, Angle Relationships G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent;

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Lesson 4.2: Angle Relationships in Triangles Learning ...4.2.pdf · Lesson 4.2: Angle Relationships in Triangles Page 223 in text ... deductive reasoning to formally prove the sum

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Basic Essay Structure Central Idea The central idea is the focus of any type of composition. It states what you are going to prove.

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Class IX - KopyKitab › ebooks › 2015 › 03 › 6670 › ... · Q16 If one angle of a parallelogram is a right angle prove that it is a rectangle. Q17. The angles of a quadrilateral

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Chapter 5 · PDF fileThe smallest angle is always opposite the _____. The largest angle is ... The shortest side is always opposite the ... Identify the statement you want to prove

Chapter 5 · PDF fileThe smallest angle is always opposite the _____. The largest angle is ... The shortest side is always opposite the ... Identify the statement you want to prove

ASA- Angle Side Angle Used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent.

ASA- Angle Side Angle Used to prove triangle congruence: if two angles and the included side of two triangles are congruent, then the triangles are congruent.

Holt Geometry 5-1 Perpendicular and Angle Bisectors Prove and apply theorems about perpendicular bisectors. Prove and apply theorems about angle bisectors.

Holt Geometry 5-1 Perpendicular and Angle Bisectors Prove and apply theorems about perpendicular bisectors. Prove and apply theorems about angle bisectors.

3.5 Proving Lines Parallel. Objectives Recognize angle conditions that occur with parallel lines Prove that two lines are parallel based on given angle.

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4.5 Prove Triangles Congruent by ASA and AAS.notebook · 2018. 9. 9. · Angle-Angle-Side (AAS) Congruence Theorem If two angles and a non-included side of one triangle are congruent

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Rapid Prototyping 1. Prototype: It is a model fabricated to prove out a concept or an idea. Prototype: It is a model fabricated to prove out a concept.

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WordPress.com€¦ · A main idea is the most important idea or claim that a text communicates. The details in a text support, prove, or illustrate the main idea. The main idea of

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yupiit.orgyupiit.org/.../integrated_math_ii_curriculum_map_base.docx · Web view* Prove the Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Same-Side Interior

yupiit.orgyupiit.org/.../integrated_math_ii_curriculum_map_base.docx · Web view* Prove the Alternate Interior Angle Theorem, Alternate Exterior Angle Theorem, Same-Side Interior

 · the Polygon Angle-Sum Theorem. Sum = (n —2)180 ... What is the measure of an interior angle of the same polygon? ... Prove the theorem. Sides

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