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Coordinate

Geometry

ProofsPolygonsTrianglesAngles

and Lines

Parallel Lines

Angles and Lines - 100

1 243

657 8

Name a pair of vertical angles.Answers: 1 and 4; 3 and 2

5 and 8; 7 and 6

Angles and Lines - 200

1 243

657 8

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

Angles and Lines - 300

1 2165

111017 16

46

1215 14

1387

213

9

Classify 4 and 13Answers: Same Side Interior Angles

Angles and Lines - 400 F

C

D

B

E

A

H

G

Name a pair of parallel planes.

Angles and Lines - 500 F

C

D

B

E

A

H

G

Name a pair of skew lines.

Parallel Lines - 100

3

12

456

87910

11

1213

s

tm

kba

14

15

m

s

If 9 15, then which two lines (if any) are parallel?Answer: t // s

Parallel Lines - 200

3

12

456

87910

11

1213

s

tm

ba

14

15

m

s

If 1 14, then which two lines (if any) are parallel?Answer: k // m

k

Parallel Lines - 300

3

12

456

87910

11

1213

s

tm

ba

14

15

m

s

k

If 13 and 12 are supplementary, then which two lines (if any) are parallel?Answer: none

Parallel Lines - 400

3

12

456

87910

11

1213

s

tm

ba

14

15

m

s

k

If 12 and 15 + 10 are supplementary, then which two lines (if any) are parallel?Answer: a // b

Parallel Lines - 500

3

12

456

87910

11

1213

s

tm

kba

14

15

m

s

If 4 1, then which two lines (if any) are parallel?Answer: a // b

Triangles - 100

Classify the triangle by its angles and sides.Answer: Acute, Scalene

14

14.5

8

19°

81°

80°

Triangles - 200

Solve for x.Answer: 57°

90°

33°

x

Triangles - 300

Which side is longest according to the given information?Answer: BA

A

B

C

60°

20° 100°

Triangles - 400

Solve for x.Answer: 79°

22°

x

Triangles - 500

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

55°

65° y° x°

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

Question: What is 5355 diagonals?

Proofs - 100Fill in the missing piece to the proof.

Statements Reasons1. m1 = m2 1. Given2. m1 = m3 2. Vertical Angles are 3. ___________ 3. Substitutionm2 = m3

Proofs - 200Provide a justification for the statement.If a // b, then m1 = m2.

Answer: If two parallel lines are cut by a transversal, then alternate exterior angles are congruent.

1 354

6 728 a

b

Proofs - 300Provide a justification for the statement.If m7 = m3, then a // b.

Answer: If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

1 354

6 728 a

b

Proofs - 400 Put the statements of the proof in order to match the reasons.

1 354

6 728a

bGiven: 1 and 7 are supplementary. Prove: m8 = m4

1. Given2. Def. of Supp. s3. Def.of a Linear Pair4. Substitution5. Reflexive6. Subtraction7. Vertical Angles are 8. Substitution

Statements: A) m8 = m4 B) m7 = m4 C) m8 = m7 D) 1 and 7 are supplementaryE) m1 + m4 = 180F) m1 + m7 = 180G) m1 = m1H) m1 + m7 = m1 + m4

DFEHGBCA

Statements Reasons

Proofs - 500 Complete the proof.18

11a

b

265

9 101413 15 16

127

3 4

s t

Given: a // b; m13 = m4Prove: s // t

1. a // b 1. Given2. m13 = m5 2. If two // lines are cut by a transversal,

then corr. ’s are .3. m13 = m4 3. Given4. m4 = m5 4. Substituion5. 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 - 200Find the midpoint between the points (3,2) and (6,4)

Answer: (4.5,3)

Coordinate Geometry - 300

Coordinate Geometry - 400Find 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 - 500Find 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 JEOPARDYCategory

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