Using Segment and Angle Addition Postulates More Proofs Using Segment and Angle Addition Postulates

State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO A. Distributive Property B. Addition Property C. Substitution Property D. Multiplication Property

State the property that justifies the statement. 2(LM + NO) = 2LM + 2NO A. Distributive Property B. Addition Property C. Substitution Property D. Multiplication Property

State the property that justifies the statement. If 2PQ = OQ, then PQ = A. Multiplication Property B. Division Property C. Distributive Property D. Substitution Property

State the property that justifies the statement. If 2PQ = OQ, then PQ = A. Multiplication Property B. Division Property C. Distributive Property D. Substitution Property

State the property that justifies the statement. mZ = mZ A. Reflexive Property B. Symmetric Property C. Transitive Property D. Substitution Property

State the property that justifies the statement. mZ = mZ A. Reflexive Property B. Symmetric Property C. Transitive Property D. Substitution Property

State the property that justifies the statement State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF. A. Reflexive Property B. Symmetric Property C. Substitution Property D. Transitive Property

State the property that justifies the statement State the property that justifies the statement. If BC = CD and CD = EF, then BC = EF. A. Reflexive Property B. Symmetric Property C. Substitution Property D. Transitive Property

Which statement shows an example of the Symmetric Property? A. x = x B. If x = 3, then x + 4 = 7. C. If x = 3, then 3 = x. D. If x = 3 and x = y, then y = 3.

Which statement shows an example of the Symmetric Property? A. x = x B. If x = 3, then x + 4 = 7. C. If x = 3, then 3 = x. D. If x = 3 and x = y, then y = 3.

2. Definition of congruent segments AB = CD 2. Proof: Statements Reasons 1. 1. Given AB  CD ___ 2. Definition of congruent segments AB = CD 2. 3. Reflexive Property of Equality BC = BC 3. 4. Segment Addition Postulate AB + BC = AC 4.

5. Substitution Property of Equality 5. CD + BC = AC Proof: Statements Reasons 5. Substitution Property of Equality 5. CD + BC = AC 6. Segment Addition Postulate CD + BC = BD 6. 7. Transitive Property of Equality AC = BD 7. 8. Definition of congruent segments 8. AC  BD ___

Prove the following. Given: AC = AB AB = BX CY = XD Prove: AY = BD

1. Given AC = AB, AB = BX 1. 2. Transitive Property AC = BX 2. 3. Given CY = XD 3. 4. Addition Property AC + CY = BX + XD 4. AY = BD 6. Substitution 6. Proof: Statements Reasons Which reason correctly completes the proof? 5. ________________ AC + CY = AY; BX + XD = BD 5. ?

A. Addition Property B. Substitution C. Definition of congruent segments D. Segment Addition Postulate

A. Addition Property B. Substitution C. Definition of congruent segments D. Segment Addition Postulate

Jamie is designing a badge for her club Jamie is designing a badge for her club. The length of the top edge of the badge is equal to the length of the left edge of the badge. The top edge of the badge is congruent to the right edge of the badge, and the right edge of the badge is congruent to the bottom edge of the badge. Prove that the bottom edge of the badge is congruent to the left edge of the badge. Given: Prove:

2. Definition of congruent segments 2. Proof: Statements Reasons 1. Given 1. 2. Definition of congruent segments 2. 3. Given 3. 4. Transitive Property 4. YZ ___ 5. Substitution 5.

Which choice correctly completes the proof? Statements Reasons 1. Given 1. 2. Transitive Property 2. 3. Given 3. 4. Transitive Property 4. 5. _______________ 5. ?

A. Substitution B. Symmetric Property C. Segment Addition Postulate D. Reflexive Property

A. Substitution B. Symmetric Property C. Segment Addition Postulate D. Reflexive Property

Justify the statement with a property of equality or a property of congruence. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate

Justify the statement with a property of equality or a property of congruence. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate

Justify the statement with a property of equality or a property of congruence. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate

Justify the statement with a property of equality or a property of congruence. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate

Justify the statement with a property of equality or a property of congruence. If H is between G and I, then GH + HI = GI. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate

Justify the statement with a property of equality or a property of congruence. If H is between G and I, then GH + HI = GI. A. Transitive Property B. Symmetric Property C. Reflexive Property D. Segment Addition Postulate

State a conclusion that can be drawn from the statement given using the property indicated. W is between X and Z; Segment Addition Postulate. A. WX > WZ B. XW + WZ = XZ C. XW + XZ = WZ D. WZ – XZ = XW

State a conclusion that can be drawn from the statement given using the property indicated. W is between X and Z; Segment Addition Postulate. A. WX > WZ B. XW + WZ = XZ C. XW + XZ = WZ D. WZ – XZ = XW

State a conclusion that can be drawn from the statements given using the property indicated. LM  NO ___ A. B. C. D.

State a conclusion that can be drawn from the statements given using the property indicated. LM  NO ___ A. B. C. D.

Given B is the midpoint of AC, which of the following is true? ___ A. AB + BC = AC B. AB + AC = BC C. AB = 2AC D. BC = 2AB

Given B is the midpoint of AC, which of the following is true? ___ A. AB + BC = AC B. AB + AC = BC C. AB = 2AC D. BC = 2AB

A construction worker measures that the angle a beam makes with a ceiling is 42°. What is the measure of the angle the beam makes with the wall? The ceiling and the wall make a 90 angle. Let 1 be the angle between the beam and the ceiling. Let 2 be the angle between the beam and the wall. m1 + m2 = 90 Angle Addition Postulate 42 + m2 = 90 m1 = 42 42 – 42 + m2 = 90 – 42 Subtraction Property of Equality m2 = 48 Substitution

Answer:

Answer: The beam makes a 48° angle with the wall.

Find m1 if m2 = 58 and mJKL = 162. B. 94 C. 104 D. 116

Find m1 if m2 = 58 and mJKL = 162. B. 94 C. 104 D. 116

At 4 o’clock, the angle between the hour and minute hands of a clock is 120º. When the second hand bisects the angle between the hour and minute hands, what are the measures of the angles between the minute and second hands and between the second and hour hands? Understand Make a sketch of the situation. The time is 4 o’clock and the second hand bisects the angle between the hour and minute hands.

Plan Use the Angle Addition Postulate and the definition of angle bisector. Solve Since the angles are congruent by the definition of angle bisector, each angle is 60°. Answer:

Plan Use the Angle Addition Postulate and the definition of angle bisector. Solve Since the angles are congruent by the definition of angle bisector, each angle is 60°. Answer: Both angles are 60°. Check Use the Angle Addition Postulate to check your answer. m1 + m2 = 120 60 + 60 = 120 120 = 120 

The diagram shows one square for a particular quilt pattern The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD. A. 20 B. 30 C. 40 D. 50

QUILTING The diagram shows one square for a particular quilt pattern QUILTING The diagram shows one square for a particular quilt pattern. If mBAC = mDAE = 20, and BAE is a right angle, find mCAD. A. 20 B. 30 C. 40 D. 50

Example 3 Given: Prove:

Proof: Statements Reasons 1. Given 1. m3 + m1 = 180; 1 and 4 form a linear pair. 2. Linear pairs are supplementary. 2. 1 and 4 are supplementary. 3. Definition of supplementary angles 3. 3 and 1 are supplementary. 4. s suppl. to same  are . 4. 3  4

In the figure, NYR and RYA form a linear pair, AXY and AXZ form a linear pair, and RYA and AXZ are congruent. Prove that NYR and AXY are congruent.

Which choice correctly completes the proof? Proof: Statements Reasons 1. Given 1. NYR and RYA, AXY and AXZ form linear pairs. 2. If two s form a linear pair, then they are suppl. s. 2. NYR and RYA are supplementary. AXY and AXZ are supplementary. 3. Given 3. RYA  AXZ 4. NYR  AXY 4. ____________ ?

A. Substitution B. Definition of linear pair C. s supp. to the same  or to  s are . D. Definition of supplementary s

A. Substitution B. Definition of linear pair C. s supp. to the same  or to  s are . D. Definition of supplementary s

2. Vertical Angles Theorem If 1 and 2 are vertical angles and m1 = d – 32 and m2 = 175 – 2d, find m1 and m2. Justify each step. Statements Reasons Proof: 1. 1 and 2 are vertical s. 1. Given 2. 1  2 2. Vertical Angles Theorem 3. m1 = m2 3. Definition of congruent angles 4. d – 32 = 175 – 2d 4. Substitution

Statements Reasons 5. Addition Property 6. Addition Property 7. Division Property m1 = d – 32 m2 = 175 – 2d = 69 – 32 or 37 = 175 – 2(69) or 37 Answer:

Statements Reasons 5. Addition Property 6. Addition Property 7. Division Property m1 = d – 32 m2 = 175 – 2d = 69 – 32 or 37 = 175 – 2(69) or 37 Answer: m1 = 37 and m2 = 37

A. B. C. D.

A. B. C. D.