Values:

Respect, Integrity, Mathematical Thinking

GOAL: MAXIMIZE UNDERSTANDING

QuadrilateralsTriangles Regular Polygons Circles

Pris

ms

Pyr

amid

s

Warm-up

1.) What types of triangles have you studied? What are characteristics of each one?

2.) Given 2 sides of a right triangle find the third side

a.) b.) c.)

3.) What is the name a theorem you might have used to solve these?When do you use it?

By side length:

By Angle Measure:

EquilateralIsosceles Scalene

Obtuse AcuteRight

2.) Given 2 sides of a triangle find the third side

a.) Use Pythagorean THM.

OR notice that triangle is isosceles & Right =>

45/45/90. We’ll come back to this method of solving in today’s lesson

2.) Given 2 sides of a triangle find the third side

b.) USE PYTHAGOREAN THM

2.) Given 2 sides of a triangle find the third side

c.) USE PYTHAGOREAN THM

OR USE SIMILAR TRIANGLES

3.) What is the name a theorem you might have used to solve these?

PYTHAGOREAN THM

When do you use it?

WITH RIGHT TRIANGLES ONLY

Review: Special Right Triangles

45 º-45 º-90 º triangle Ex. 1.) From warmup.

Review: Special Right Triangles

45 º-45 º-90 º triangle

Review: Special Right Triangles

45 º-45 º-90 º triangle Ex. #3.)

Answers :EXACT & dominator rationalized

Review: Special Right Triangles

30º-60 º-90 º triangle

Example From the Warmup

60º

30º

Review: Special Right Triangles

30º-60 º-90 º triangle

Formula: X is the SHORT SIDE:

Review: Special Right Triangles

30º-60 º-90 º triangle

Formula: X is the SHORT SIDE:

60º

30º

Area of Triangles:

= ½ b*h

b is length of the base

h is height of triangle

63

ba

3√2

Find a & b

WARM-UP

Triangles_Area wkst #1 1.) Find the third side of the RIGHT triangle. Show your work. EXACT ANSWERS ONLY PLEASE a.) b.) c.)

7 3 12 12 ½ ¾ 4 √23 3√15 ( √5)/4 2.) Find the missing sides a.) b.) c.) 24 20/3 3 5 18 16/3 4 30 4 d.) Notice anything special about these triangles? (Hint: Look at the ratio of their corresponding sides) They are similar as the ratio of the corresponding sides is equal to 3:4 3.) Find the two missing sides a.) b.) c.) 2√2 5√2 45 45 2 2√2 5 5 2√2 4 45 2

1.) What’s wrong with this picture? It’s impossible to have a triangle with sides 15,5, 8 because 5+8 < 15 and the side would not touch.

5

15

2.) Finish the Theorems by filling in the blanks, then complete the picture that shows

these statements are true. a.) The sum of the interior angles of a triangle equals _____ 0180 _____.

b.) The exterior angle of a triangle _the sum_ of the two non-Adjacent

angles.

c.) The length of a side of a triangle is _less than_____ the sum of the

lengths of the other two sides and ___greater than_____ the difference of the lengths of the other two sides.

c-b ________ < a < ___c+b________

5.) Define the following:

a.) Angle bisector: _A line from the vertex that divides the angle into two congruent angles_. b.) Altitude:_____ A line from the vertex angle perpendicular to the opposite side _. c.) Median:__ A segment from a vertex to the midpoint of the opposite side. d.) Perpendicular bisector:___ A line that is perpendicular to the segment at its midpoint.

1.) Topic you didn’t understand & what specifically about this problem didn’t you get

2.) What you did to figure out answer (name of example from notes or book that you looked at) & why this didn’t help

3.) Plan to gain understanding of this problem & topic.

Area of Triangles:

= ½ b*h

ANY TRIANGLE:

Area of Triangles:

= ½ b*h

Height may be outside triangle

Example: Find Area of Triangle

A.) B.)

3ins

60º 60º

Area of a Equilateral Triangle in terms of side length:

Example: Find Area of Triangle

150º 15º

15º

7in