Brett Solberg – AHS – ’11-’12

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Presentation transcript:

Brett Solberg – AHS – ’11-’12 4.3 & 4.4 Geometry Brett Solberg – AHS – ’11-’12

Warm-up Solve for a, b, and c. Justify your reasoning. a b c 40° 65°

Today’s Objectives Parallel and Perpendicular Lines. Triangles Relationships to each other. Triangles Triangle Sum Theorem Classification Exterior Angle Theorem

Fill In the Blanks Any friend of yours is… a friend of mine. The enemy of my enemy is… my friend. The enemy of my friend is… my enemy. Friends = Lines that are parallel Enemies = Lines that are perpendicular

Theorem 3.9 l m n If two lines are parallel to the same line, then they are parallel to each other. l m n

Theorem 3.10 l m n If two lines are perpendicular to the same line, then they are parallel to each other. l m n

Theorem 3.11 If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other line. l m n

Worksheet Example #6 How are a and e related? a || b, b || c, c | d, d || e a b c d e

Worksheet You have 15 minutes to work on the worksheet.

Triangles What is the sum of the angles in the triangle? a b c 40° 65°

Triangle Angle Sum Theorem The sum of the angles in any triangle is 180°. 80° 40° 60° 40 + 80 + 60 = 180

Triangle Classifications Triangles are classified by their angles and the number of congruent sides.

Acute Triangle Triangle where the measure of every angle is less than 90°.

Obtuse Triangle Triangle where one angle measure is greater than 90°.

Right Triangle Triangle with one angle measure equal to 90°.

Equiangular Triangle Triangle where all angles are congruent. What would the measure of the angles be?

Scalene Triangle Triangle where no side lengths are congruent.

Isosceles Triangle Triangle where two side lengths are congruent.

Equilateral Triangle Triangle where all three side lengths are congruent.

Classify the Triangles By angles.

Classify the Triangles By Side Lengths

Exterior Angle An angle formed by the side of a triangle and the extension of the adjacent side. Exterior Angle

Remote Interior Angles The two angles inside the triangle which are not adjacent to the exterior angle. Exterior Angle Remote Interior Angles

Triangle Exterior Angle Theorem The measure of the exterior angle is equal to the sum of the remote interior angles. Exterior Angle Remote Interior Angles 40 80 120 40 + 80 = 120

Example Find x, y, and z. 55 + 90 + x = 180 by Triangle Angle Sum Thm. y = 55 + 90 by Exterior Angles Thm. 10 + y + z = 180 by Triangle Angle Sum Thm. 55 10 x y z

Worksheet Both worksheets are due by next class.