Coordinate Geometry ProofsPolygonsTriangles Angles and Lines Parallel Lines

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

Angles and Lines Name a pair of alternate interior angles. Answers:  3 and  6;  4 and  5

Angles and Lines Classify  4 and  13 Answers: Same Side Interior Angles

Angles and Lines Name a pair of parallel planes.

Angles and Lines Name a pair of skew lines.

Parallel Lines s t m k b a m s If  9   15, then which two lines (if any) are parallel? Answer: t // s

Parallel Lines s t m b a m s If  1   14, then which two lines (if any) are parallel? Answer: k // m k

Parallel Lines s t m b a m s k If  13 and  12 are supplementary, then which two lines (if any) are parallel? Answer: none

Parallel Lines s t m b a m s k If  12 and  15 +  10 are supplementary, then which two lines (if any) are parallel? Answer: a // b

Parallel Lines s t m k b a m s If  4   1, then which two lines (if any) are parallel? Answer: a // b

Triangles Classify the triangle by its angles and sides. Answer: Acute, Scalene ° 81° 80°

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

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

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

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

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

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

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

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

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

Proofs Fill in the missing piece to the proof. StatementsReasons 1. m  1 = m  21. Given 2. m  1 = m  3 2. Vertical Angles are  3. ___________3. Substitution m  2 = m  3

Proofs Provide a justification for the statement. If a // b, then m  1 = m  2. Answer: If two parallel lines are cut by a transversal, then alternate exterior angles are congruent a b

Proofs Provide a justification for the statement. If m  7 = m  3, then a // b. Answer: If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel a b

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

Statements Reasons Proofs Complete the proof a b s t Given: a // b; m  13 = m  4 Prove: s // t 1. a // b 1. Given 2. m  13 = m  5 2. If two // lines are cut by a transversal, then corr.  ’s are . 3. m  13 = m  4 3. Given 4. m  4 = m  5 4. Substituion 5. s // t 5. If two lines are cut by a transversal and alt. ext.  ’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 Find the midpoint between the points (3,2) and (6,4) Answer: (4.5,3)

Coordinate Geometry - 300

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