2x

4y

102

x + 4y

2x + 4y = 102 x + 4y + 102= 180

2x = 102 - 4y 51 – 2y + 4y + 102 = 180

2y + 153 = 180

2y = 27

x = 51 - 2y

x = 51 – 2(13.5)

x = 51 – 27

x = 24y = 13.5

81

x + 86 + 56 + 81 + 88 = 360

x + 311 = 360

x = 49

Chapter 3 REVIEW!

Chapter 3 Test Next Class!

Triangles

Triangle Sum Theorem

• The sum of the angles of a triangle is 180 Degrees!

If 2 angles of 1 triangle are congruent to 2 angles of another triangle, then the angels are congruent.

The exterior angle of a triangle equals the sum of the remote interior angles.

Acute angles of a right triangle are complementary

At most, there is one obtuse angle or one right angle in a triangle.

Angles of an equiangular triangle equal 60 degrees.

POLGYONS

INTERIOR ANGLE SUM

Sum of the interior angles of a polygon with n sides

EXTERIOR ANGLE SUM

Sum of the exterior angles of a polygon with n sides

EACH INTERIOR ANGLE

Each of the interior angles of a polygon with n sides

EACH EXTERIOR ANGLE

Each of the exterior angles of a polygon with n sides

Vocabulary Practice!

True or False

Parallel Lines

Parallel lines are noncoplanar lines that do not intersect.

FALSE

Parallel lines are COPLANAR lines that do not intersect!

Skew Lines

Skew lines are noncoplanar lines. Therefore, they are neither parallel nor intersecting.

TRUE

Same-Side Interior Angles

If a transversal cuts two lines, same side interior angles are supplementary.

FALSE

If a transversal cuts two PARALLEL lines, same side interior angles are supplementary.

Corresponding Angles

If a transversal cuts two parallel lines, corresponding angles are supplementary.

FALSE

If a transversal cuts two parallel lines, corresponding angles are congruent.

Alternate Interior Angles

If a transversal cuts two parallel lines, alternate interior angles are congruent.

TRUE

Alternate Interior Angles

Alternate interior angles are always congruent.

FALSE

They are only congruent if the lines are parallel.

Triangle

In triangle ABC, <A = 91. Triangle <ABC could be a right triangle.

FALSE

At most, there is one obtuse angle or one right angle in a triangle.

Triangle

In triangle ABC, <A = 90. <B and <C are complementary

TRUE

Triangle

This is a scalene triangle:

5 5

5FALSE

This is an EQUILATERAL triangle.

Triangle

This is an isosceles triangle:

5 5

5

An isosceles has AT LEAST 2 congruent sides.

TRUE

PROVING LINES PARALLEL

Ways to Prove Two Lines Parallel

1. Show that a pair of CA are congruent.

2. Show that a pair of AI angles are congruent.

3. Show that a pair of SSI angles are supplementary.

4. Show that a pair of lines are perpendicular to the same line.

5. Show that both lines are parallel to a third line.

What is on my Test???

• True and False

• Finding values of x and y in triangle diagrams and in parallel line diagrams

• Finding CA, SSI, AI and Vertical angles & their transversals

• Polygon angle values

• 1 fill in the blank proof

• 1 completely blank proof about parallel lines

Homework

• Worksheet

• Pg 111 •1-19 all

• Pg 112•1-12all