Angles and Lines Parallel Lines Triangles Polygons Proofs

Angles and Lines Parallel Lines Triangles Polygons Proofs Coordinate Geometry 100 100 100 200 200 200 300 300 300 400 400 400 500 500 500

Angles and Lines - 100 1 2 3 4 5 6 7 8 Name a pair of vertical angles. Answers: Ð 1 and Ð 4; Ð 3 and Ð 2 Ð 5 and Ð 8; Ð 7 and Ð 6

Angles and Lines - 200 1 2 3 4 5 6 7 8 Name a pair of alternate interior angles. Answers: Ð 3 and Ð 6; Ð 4 and Ð 5

Angles and Lines - 300 1 2 1 3 4 5 16 6 2 7 8 9 10 11 17 16 13 15 14 12 Classify Ð 4 and Ð 13 Answers: Same Side Interior Angles

Angles and Lines - 400 Name a pair of parallel planes.

Angles and Lines - 500 Name a pair of skew lines.

Parallel Lines - 100 k b a 1 13 12 15 6 5 10 11 4 9 3 7 8 m 2 s m t s 14 If Ð 9 @ Ð 15, then which two lines (if any) are parallel? Answer: t // s

Parallel Lines - 200 k b a 1 13 12 15 6 5 10 11 4 9 3 7 8 m 2 s m t s 14 If Ð 1 @ Ð 14, then which two lines (if any) are parallel? Answer: k // m

Parallel Lines - 300 k b a 1 13 12 15 6 5 10 11 4 9 3 7 8 m 2 s m t s 14 If Ð 13 and Ð 12 are supplementary, then which two lines (if any) are parallel? Answer: none

Parallel Lines - 400 k b a 1 13 12 15 6 5 10 11 4 9 3 7 8 m 2 s m t s 14 If Ð 12 and Ð 15 + Ð 10 are supplementary, then which two lines (if any) are parallel? Answer: a // b

Parallel Lines - 500 k b a 1 13 12 15 6 5 10 11 4 9 3 7 8 m 2 s m t s 14 If Ð 4 @ Ð 1, then which two lines (if any) are parallel? Answer: a // b

Triangles - 100 14 81° 19° 14. 5 80° 8 Classify the triangle by its angles and sides. Answer: Acute, Scalene

Triangles - 200 33° 90° Solve for x. Answer: 57° x

Triangles - 300 B 60° A 20° 100° C Which side is longest according to the given information? Answer: BA

Triangles - 400 22° x Solve for x. Answer: 79°

Triangles - 500 55° 65° y° x° Solve for x and y. Answer: x = 120° y = 60°

Polygons - 100 Answer: The sum of the interior angles of this figure is 720. Question: What is a hexagon?

Polygons - 200 Answer: The number of diagonals that can be drawn in this figure is 2. Question: What is a quadrilateral?

Polygons - 300 Answer: This is the sum of the exterior angles of any convex polygon. Question: What is 360°?

Polygons - 400 Answer: The sum of the interior angles of this figure is 900. Question: What is a heptagon?

Polygons - 500 Answer: This is the number of diagonals that could be drawn in a polygon with 105 sides. Question: What is 5355 diagonals?

Proofs - 100 Fill in the missing piece to the proof. Statements Reasons 1. mÐ 1 = mÐ 2 1. Given 2. mÐ 1 = mÐ 3 2. Vertical Angles are @ mÐ 2 = mÐ 3 3. ______ 3. Substitution

Proofs - 200 Provide a justification for the statement. If a // b, then mÐ 1 = mÐ 2. 4 8 6 2 7 1 5 3 Answer: If two parallel lines are cut by a transversal, then alternate exterior angles are congruent. b a

Proofs - 300 Provide a justification for the statement. If mÐ 7 = mÐ 3, then a // b. 4 8 6 2 7 1 5 3 Answer: If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. b a

Proofs - 400 Statements: Put the statements of the proof in order to match the reasons. A) mÐ 8 = mÐ 4 B) mÐ 7 = mÐ 4 C) mÐ 8 = mÐ 7 D) Ð 1 and Ð 7 are supplementary E) mÐ 1 + mÐ 4 = 180 F) mÐ 1 + mÐ 7 = 180 G) mÐ 1 = mÐ 1 H) mÐ 1 + mÐ 7 = mÐ 1 + mÐ 4 Given: Ð 1 and Ð 7 are supplementary. Prove: mÐ 8 = mÐ 4 b a 8 6 2 4 7 D 1. Given F 2. Def. of Supp. Ðs E 3. Def. of a Linear Pair H 4. Substitution G 5. Reflexive B 6. Subtraction C 7. Vertical Angles are @ A 8. Substitution 1 5 3

Proofs - 500 Complete the proof. 1 2 a Given: a // b; mÐ 13 = mÐ 4 Prove: s // t Statements 3 4 5 6 7 8 9 10 11 12 b 13 14 15 16 t Reasons s 1. a // b 1. Given 2. mÐ 13 = mÐ 5 2. If two // lines are cut by a transversal, then corr. Ð’s are @. 3. mÐ 13 = mÐ 4 3. Given 4. mÐ 4 = mÐ 5 4. Substituion 5. s // t 5. If two lines are cut by a transversal and alt. ext. Ð’s are @, then the lines are //. It can be done in 5 steps if you split the givens into 2 steps.

Coordinate Geometry - 100

Coordinate Geometry - 200 Find the midpoint between the points (3, 2) and (6, 4) Answer: (4. 5, 3)

Coordinate Geometry - 300

Coordinate Geometry - 400 Find the midpoint between (2, 7) and (1, 15). Find the slope of the line that runs through those two points. Answer: (3/2, 11) and 8

Coordinate Geometry - 500 Find the midpoint, slope, parallel slope, and perpendicular slope for the following points. (4, 7) and (-1, 3) Answer: (3/2, 5) – 4/5 - -5/4

FINAL JEOPARDY Category Parallel Lines

What are the five ways we can prove lines are parallel? • Two lines cut by a transversal and corr angles congruent • Two lines cut by transversal and alt int angles congruent • Two lines cut by a transversal and same-side int angles are supplementary • Two lines perpendicular to the same line • Alt ext angles are congruent