2.1:Triangles Properties - properties M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems.

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Presentation transcript:

2.1:Triangles Properties - properties M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts GSE’s

Triangles Triangle-figure formed by 3 segments joining 3 noncollinear pts. Triangles are named by these three pts (ΔQRS) Would it matter if you named in a different order? Nope! ΔRQS, ΔSRQ all mean the same thing Q R S

Parts of a Triangle Sides A B C Segment AB, AC, BC Points A, B, C Angles A, B, C Angles Vertices

2 Ways to classify triangles 1) by their Angles 2) by their Sides

1)Angles Acute- Obtuse- Right- Equiangular- all 3 angles less than 90 o one angle greater than 90 o, less than 180 o One angle = 90 o All 3 angles are congruent

2) Sides Scalene Isosceles Equilateral - No sides congruent -2 sides congruent - All sides are congruent

Parts of a Right Triangle Leg Hypotenuse Sides touching the 90 o angle Side across the 90 o angle. Always the largest in a right triangle

Legs – the congruent sides Isosceles Triangle A B C Leg Base-Non congruent side Across from the vertex Vertex- Angle where the 2 congruent sides meet Base Angles: Congruent Formed where the base meets the leg

Triangle ABD is isosceles with A as the vertex. If AB = 10 in, and BD = 12 in What is the perimeter of Triangle ABD?

Example Triangle TAP is isosceles with angle P as the Vertex. TP = 14x -5, TA = 6x + 11, PA = 10x Is this triangle also equilateral? TA P 14x-5 6x x + 43 TP PA 14x – 5 = 10x x = 48 X = 12 TP = 14(12) -5 = 163 PA= 10(12) + 43 = 163 TA = 6(12) + 11 = 83

1. 2.

Example BCD is isosceles with BD as the base. Find the perimeter if BC = 12x-10, BD = x+5 CD = 8x+6 B C D base 12x-108x+6 X+5 Ans: 12x-10 = 8x+6 X = 4 Re-read the question, you need to find the perimeter 12(4) (4)+6 38 (4)+5 9 Perimeter = = 85 Final answer

Example 2 Solve for x. 5x +24 Ans: (5x+24) + (5x+24) + (4x+6) = 180 5x x x+6 = x + 54 = x = 126 x = 9

Assignment