Download Chapter 6 Quiz 2 – Section 6C – Review Sheet

 Math 2: Algebra 2, Geometry and Statistics
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Chapter 6 Quiz 2 – Section 6C – Review Sheet Students Will Be Able To: • Read and write proofs in the following styles: Chinese Outline, Russian Outline, Paragraph Proof, Two-­‐Column Proof. • Given a written description, draw a diagram and set up a proof • Write proofs with detours (in other words, that use triangle congruence as a means of proving something else.) DO NOW: For each of the following situations, draw and label a diagram and write the given and prove statements needed. 1. The angle bisectors of the base angles of an isosceles triangle are congruent. Diagram 2. If a segment is the median to the base of an isosceles triangle, then it bisects the
vertex angle of the triangle. Diagram 3. If two triangles are congruent, then the corresponding medians are congruent. Diagram Median – a segment from the midpoint of one side of a triangle to the opposite vertex. Altitude – a segment perpendicular to one side of a triangle, through the opposite vertex. Midsegment – a segment connecting the midpoints of two sides of a triangle. Math 2: Algebra 2, Geometry and Statistics
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Reference Information: Hint: One of the best ways of figuring out how to write a proof is to work backwards from the conclusion. Ask yourself the following questions: 1) What am I trying to prove? Congruent triangles? Congruent segments? Congruent angles? Another relationship? (Isosceles triangles, midpoints, bisectors, etc.) 2) What are the possible methods of proving that? Congruent triangles -­‐ SSS, SAS, ASA, AAS (and HL in Ch 6.13) Congruent segments -­‐ CPCTC Congruent angles -­‐ CPCTC Another relationship -­‐ fulfill the needs of a definition or a theorem 3) Is this method likely to work here? Are there triangles with the parts you want? Which ones? 4) Do I have enough information to prove the triangles are congruent? Label the figure with known information (given as well as inferred). Do the triangles share a side or angle so that it is congruent in both triangles? 5) Did I use all of the given information? Does the information given apply more to another pair of triangles? 6) Does every step serve a purpose? Do you have steps that don’t lead anywhere (except the conclusion)? 7) Does each step have a valid reason? Does it lead to another step correctly? Math 2: Algebra 2, Geometry and Statistics
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Reasons for CONGRUENT TRIANGLES: SAS (Side-­‐Angle-­‐Side) ASA (Angle-­‐Side-­‐Angle) SSS (Side-­‐Side-­‐Side) AAS (Angle-­‐Angle-­‐Side) HL (Hypotenuse-­‐Leg) Reasons for CONGRUENT ANGLES: Halves of equal angles are equal Reflexive (shared angle) Definition of Angle Bisector (forms equal adjacent angles) Definition of Perpendicular (forms equal adjacent right angles) Definition of Equiangular ITT (Isosceles Triangle Theorem if two sides are the same, then two base angles are the same) Vertical Angles (also called Opposite Angles) CPCTC (Corresponding Parts of Congruent Triangles are Congruent) Corresponding Angles of Parallel Lines Alternate Interior Angles of Parallel Lines Alternate Exterior Angles of Parallel Lines Reasons for CONGRUENT SEGMENTS: Halves of congruent segments are congruent. Reflexive (shared side) Definition of Midpoint Definition of Isosceles Definition of Equilateral ITT (Isosceles Triangle Theorem -­‐ if two base angles are the same, then two sides are the same) CPCTC (Corresponding Parts of Congruent Triangles are Congruent) Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
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Practice Problems: You may use any method of proof you choose. If you use a flowchart proof, you must add reasons for anything that isn’t a definition. O
1. Given: ∠SLA = ∠SAL ∠ARL = ∠LOA S
Prove: ∠𝑅𝐿𝐴 ≅ ∠𝑂𝐴𝐿 L
R
A
2. Given: ∠𝐹𝐸𝐷 ≅ ∠𝐴𝐵𝐶, ∠𝐷𝐹𝐸 ≅ ∠𝐶𝐴𝐵, 𝐹𝐸 ≅ 𝐵𝐴 E
Prove: 𝐹𝐷 || 𝐶𝐴 F
3. Given: WITCH is equilateral and equiangular. D
A
C
B
H
Prove: ΔITY is isosceles. C
W
Y
4. Complete two of the proofs you set up in the do now. I
T