'Vertical angles congruence theorem' presentation slideshows

Geometry Cliff Notes

Geometry Cliff Notes. Chapters 4 and 5. Chapter 4 Reasoning and Proof, Lines, and Congruent Triangles. Distance Formula. d= Example: Find the distance between (3,8)(5,2) d=. Midpoint Formula. M= Example:

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Geometry Cliff Notes

Geometry Cliff Notes. Chapters 4 and 5. Chapter 4 Reasoning and Proof, Lines, and Congruent Triangles. Distance Formula. d= Example: Find the distance between (3,8)(5,2) d=. Midpoint Formula. M= Example:

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Assignment

Assignment. P. 526-529: 1-11, 15-21, 33-36, 38, 41, 43 Challenge Problems. Proving Lines Parallel. Proving Triangles Congruent. Proving Triangles Congruent. Four Window Foldable.

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January 5, 2011

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EXAMPLE 1

REASONS. STATEMENT. EXAMPLE 1. Use right angle congruence. Theorem: Right Angle Congruence Theorem All right angles are congruent Given: <1 and <2 are right angles Prove: <1 is congruent to <2. AB BC , DC BC. GIVEN:. B C. PROVE:. REASONS. STATEMENT. 1. 1. AB BC , DC BC. Given.

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4.7 Isosceles and Equilateral Triangles

4.7 Isosceles and Equilateral Triangles. Objective: You will use theorems about isosceles and equilateral triangles. Base Angle Theorem. If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem.

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Warm Up

Use Isosceles and Equilateral Triangles. Warm Up. Lesson Presentation. Lesson Quiz. equilateral. scalene. ANSWER. ANSWER. isosceles. ANSWER. Warm-Up. Classify each triangle by its sides. 1. 2 cm, 2 cm, 2 cm. 2. 7 ft, 11 ft, 7 ft. 3. 9 m, 8 m, 10 m.

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EXAMPLE 1

AB BC , DC BC. GIVEN:. B C. PROVE:. REASONS. STATEMENT. 1. 1. AB BC , DC BC. Given. 2. 2. Definition of perpendicular lines. B and C are right angles. 3. B C. 3. Right Angles Congruence Theorem. EXAMPLE 1. Use right angle congruence. Write a proof.

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EXAMPLE 3

Prove that if two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel. ? 4 ? 5. GIVEN :. g h. PROVE :. EXAMPLE 3. Prove the Alternate Interior Angles Converse. SOLUTION. REASONS. STATEMENTS. 1 . . g h. 1 . . Given. 2 . .

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EXAMPLE 3

ALGEBRA. Find the values of x and y in the diagram. STEP 1. Find the value of y . Because KLN is equiangular, it is also equilateral and KN KL . Therefore, y = 4. STEP 2.

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EXAMPLE 3

ALGEBRA. Find the values of x and y in the diagram. STEP 1. Find the value of y . Because KLN is equiangular, it is also equilateral and KN KL . Therefore, y = 4. STEP 2.

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EXAMPLE 3

ALGEBRA. Find the values of x and y in the diagram. STEP 1. Find the value of y . Because KLN is equiangular, it is also equilateral and KN KL . Therefore, y = 4. STEP 2.

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Justifications for proofs

Justifications for proofs. 2.6 & 2.7. Definition of midpoint: the point that bisects the line segment. Right Angle Congruence Theorem: All right angles are congruent . Congruent Supplements Theorem: If two angles are supplementary to the same angle, then they are congruent .

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EXAMPLE 1

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EXAMPLE 1

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