1.3: Angles -angle pairs GSE

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Presentation transcript:

1.3: 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

Activity (handout): – Exploring Angle Relationships Questions 1 - 7

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

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

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

5) Complementary Angles Complementary Angles – the sum of the 2 angles is 90o 58 + 32 = 180

Find the unknown angle measures

Handout – Part II

In class practice Complementary & supplementary angles Page 70: 1-10, 15-28 Vertical angles Page 78: 1-33, 51-53

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

Angle Bisector A ray that divides an angle into 2 congruent adjacent angles. A Angle ABD is CONGRUENT to angle DBC D B C

Ex: If FH bisects <EFG & m<EFG=120o, what is m<EFH?

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?

In class practice Angle bisectors Page 64: 1-22, 28-30 Homework: Worksheets 2.2A, 2.3A, 2.4A