Unit 8 Chapter 3 Properties of Angles and Triangles
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1 Unit 8 Chapter 3 Properties of Angles and Triangles May 16 7:01 PM Types of lines 1) Parallel Lines lines that do not (and will not) cross each other are labeled using matching arrowheads are always the same distance apart If we label the lines AB and CD and we know they are parallel, then we can write AB CD 1
2 2) Perpendicular Lines lines that cross each other at right angles. often are marked with a right angle symbol. May 16 7:21 PM 2) Transversal a line that crosses two or more parallel lines When a transversal crosses two lines 8 angles are formed May 16 7:09 PM 2
3 Exterior Angles Any angles formed by a transversal and two lines that lie outside the lines Interior Angles Any angles formed by a transversal and two lines that lie inside the parallel lines Corresponding Angles One interior angle and one exterior angle that are on the same side of the transversal but are not adjacent. May 16 7:12 PM Pairs of Angles 1) Supplementary Angles two angles that add up to 180º they form a straight angle (line)
4 2) Complementary Angles two angles that add up to 90º they form a right angle. May 16 7:23 PM 3) Vertically Opposite Angles a pair of angles formed by two lines that intersect. these angles are equal in measure. May 16 7:24 PM 4
5 Example 1: Determine the measure of each unknown angle. Explain why. May 16 7:25 PM 1) Corresponding Angles angles that would fit on top of each other if you slide one of the parallel lines on top of the other. One is interior and one is exterior Corresponding angles are equal. The diagram below shows 4 pairs of corresponding angles: Hints: Look for the F Mar 20 1:17 PM 5
6 2) Alternate exterior Angles Angles that are outside the parallel lines and on different sides of the transversal Alternate exterior angles are equal. The diagram below shows 2 pairs of alternate exterior angles: Mar 20 1:51 PM 3) Alternate interior Angles Angles that are inside the parallel lines and on different sides of the transversal Alternate interior angles are equal. The diagram below shows 2 pairs of alternate interior angles: Hints: Look for the "z" Shape Mar 20 1:59 PM 6
7 4) Same side interior Angles Angles that are inside the parallel lines and on same side of the transversal Same side interior angles are supplementary. (add up to 180º) The diagram below shows 2 pairs of same side interior angles: Hints: Look for the "C" shape Mar 20 2:01 PM 5) Same side exterior Angles Angles that are outside the parallel lines and on same side of the transversal Same side exterior angles are supplementary. (add up to 180º) The diagram below shows 2 pairs of same side exterior angles: Mar 20 2:02 PM 7
8 Ex) In the diagram below name a pair of: A) Corresponding angles B) Alternate exterior angles C) Alternate interior angles D) Same side interior angles E) Same side exterior angles Mar 20 2:03 PM Example 1: Determine the missing measures and state a reason for your answer. d) 8
9 Example 2: Solve for x and find the measure of each indicated angle. a) b) c) May 16 6:59 PM 9
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