# Triangles, Quadrilaterals, & Circles

## Triangles

What is a triangle?A triangle is a three sided polygon.

What are the different types of triangles?

Equilateral Triangle: All Three Sides Are Congruent.

Isosceles Triangle: Two Sides Are Of Equal Length.

Scalene Triangle: No Sides Are Congruent

Right Triangle: One Angle Is A Right Angle.

Acute Triangle: All Angles Are Acute.

Obtuse Triangle: One Angle is An Obtuse Angle.

What is the formula for finding the area of a triangle?

A = 1/2 bh

b = base, h = height

## Types Of Triangles

## Proportional Sides of Similar Triangles

What are congruent triangles?Congruent triangles have the same size and shape.

What are similar triangles?

Similar triangles have the same shape but not necessarily the same size.

What are corresponding sides of triangles?

The corresponding sides of triangles are the sides that match.

How do we find a missing of corresponding triangles?

Pattern Method:

Step 1: Find The Corresponding Sides In Both Triangles

AB = EF

BC = FG

AC = EG

Step 2: Set up a ratio of the corresponding sides.

AB & EF = 3/6

BC & FG = 5/? (Missing Side)

AC & EG = 4/8

Step 3: Ask what is the pattern? (What is being done to the sides of the first triangle to get to the sides of the second?

Answer: Multiplying By 2.

So the missing side of the second triangle is 10m.

Proportion Method:

Step 1: Pick two corresponding sides.

AB & EF

Step 2: Write the corresponding sides as a ratio.

AB/EF = 3/6

Step 3: Set up a proportion to find the missing side.

3/6 = 5/x

Step 4: Cross multiply.

3x = 30

x = 10

So the missing side = 10m.

## Quadrilaterals

What is a quadrilateral?A quadrilateral is a four sided polygon.

What are the different types of quadrilaterals?

Square: Opposite sides are parallel, all sides are congruent, has 4 right angles.

Rectangle: Opposite sides are parallel, opposite sides are congruent, has 4 right angles.

Parallelogram: Opposite sides are parallel and congruent.

Rhombus: All sides are parallel and congruent.

Trapezoid: Only 1 pair of sides are parallel.

What are the formulas for finding the area of quadrilaterals?

Square:

A = s2

s = side length

Rectangle:

A = lw

l = length, w = width

Parallelogram/Rhombus:

A = bh

b = base, h = height

Trapezoid:

A = 1/2h(b1 + b2)

h = height, b1 = length of top base, b2 = length of bottom base

## Types Of Quadrilaterals

## Circles

What is a circle?A circle consists of all points in a plane that are an equal distance from a given point.

What is a radius?

Any segment from the center point of the circle to a point on the circle. The radius is ½ of the diameter.

What is a diameter?

Any segment that passes through the center point of the circle and has both endpoints on the circle. The diameter of a circle is twice as long as the radius.

What is a chord?

A line segment that has both endpoints on the circle.

What is a central angle?

An angle with its vertex at the center of the circle and sides that are radii of the circle.

What is circumference?

Circumference (C) is the distance around the circle.

What is π?

π is the ratio of the circumference of a circle to its diameter. It is approximately 3.14 no matter how large or small the circle is. When working with π we do not use 3.14. We ALWAYS leave our answers in terms of π.

What is the formula for finding the circumference of a circle?

C = πd or C = 2πr

d = diameter

r = radius

The formula you use depends on the information that is given in the problem.

What is the formula for finding the area of a circle?

A = πr2

r = radius

What is a sector?

A sector is a region of a circle that is bounded by two radii and an arc of the circle.

What is the formula for finding the area of a sector?

x/360 = πr2

x = the measure of the arc of a sector

r = the radius of the circle