4 3 4 4 GEOMETRY Brett Solberg AHS
4. 3 & 4. 4 GEOMETRY Brett Solberg – AHS – ’ 11 -’ 12
Warm-up Solve for a, b, and c. Justify your reasoning. a 40° b c 65°
Today’s Objectives Parallel and Perpendicular Lines. � 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 If two lines are parallel to the same line, then they are parallel to each other. l m n
Theorem 3. 10 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 40° c 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 where the measure of every angle is less than 90°.
Obtuse Triangle where one angle measure is greater than 90°.
Right Triangle with one angle measure equal to 90°.
Equiangular Triangle where all angles are congruent. What would the measure of the angles be?
Scalene Triangle where no side lengths are congruent.
Isosceles Triangle where two side lengths are congruent.
Equilateral 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. s e gl n A r R ot em e io r e t In Exterior Angle
Triangle Exterior Angle Theorem The measure of the exterior angle is equal to the sum of the remote interior angles. s e gl n A r R ot em e io r e t In 80 Exterior Angle 40 40 + 80 = 120
Example Find x, y, and z. 55 10 x y 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.
Worksheet Both worksheets are due by next class.
- Slides: 26