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 90o

one angle greater than 90o, less than 180o

One angle = 90o

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

Leg

Hypotenuse

Sides touching the 90o 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?

ExampleTriangle TAP is isosceles with angle P as the Vertex. TP = 14x -5 , TA = 6x + 11 , PA = 10x + 43. Is this triangle also equilateral?

T A

P

14x-5

6x + 11

10x + 43

TP PA

14x – 5 = 10x + 43

4x = 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-10 8x+6

X+5

Ans: 12x-10 = 8x+6

X = 4

Re-read the question, you need to find the perimeter

12(4)-10

38

8(4)+6

38

(4)+5

9

Perimeter =38 + 38 + 9 = 85Final answer

Example 2

Solve for x .

5x +24

Ans: (5x+24) + (5x+24) + (4x+6) = 180

5x +24 + 5x+ 24 + 4x+6 = 180

14x + 54 = 180

14x = 126

x = 9

Assignment