Angles -angle pairs GSE

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Presentation transcript:

Angles -angle pairs GSE M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines

Types of Angle Relationships Adjacent Angles Vertical Angles Linear Pairs Supplementary Angles Complementary Angles

1) Adjacent Angles Adjacent Angles - Angles sharing one side that do not overlap 2 1 3

2)Vertical Angles Vertical Angles - 2 non-adjacent angles formed by 2 intersecting lines (across from each other). They are CONGRUENT !! 1 2

3) Linear Pair Linear Pairs – adjacent angles that form a straight line. Create a 180o angle/straight angle. 2 1 3

4) Supplementary Angles Supplementary Angles – two angles that add up to 180o (the sum of the 2 angles is 180) Are they different from linear pairs?

5) Complementary Angles Complementary Angles – the sum of the 2 angles is 90o

Angle Bisector A ray that divides an angle into 2 congruent adjacent angles. BD is an angle bisector of <ABC. A D B C

Last example: Solve for x. BD bisects ABC A D x+40o x+40=3x-20 40=2x-20 60=2x 30=x 3x-20o C B Why wouldn’t the Angle Addition Postulate help us solve this initially?

Solve for x and find the m<1

Solve for x and find the m<1

Find x and the

Assignment