5-8 Special Right Triangles Learning Goal: Apply the properties of 45-45-90 & 30-60-90 triangles in simplest radical form

Exploration What is special about the triangles created by folding a square at its diagonal? What is special about the triangles created by folding an equilateral triangle in half? Work with your partner to complete the investigation sheet. Leave answers in SIMPLEST RADICAL FORM.

Observations Let’s compare your answers with the class What observations do you notice about the side lengths and angles of the triangles created by folding a square at its diagonal? What observations do you notice about the side lengths and angles of the triangles created by folding an equilateral triangle in half? Turn to workbook pg227-228 to use variables!

45o - 45o - 90o Triangles Notes Formulas Let x = length of the legs Legs are the same length Hyp = leg Hypotenuse 450 Leg x x 450 x Leg

30o - 60o - 90o Triangles Notes Formulas Let x = length of shortest leg Hyp = 2(short) Long= Short Short leg is always opposite 300 Long leg is always opposite 600 Hypotenuse 300 2x Long Leg x 600 x Short leg

Workbook Examples Turn to page 229 and complete example 3

Example 4: Calculate the length of the missing sides 450 16cm

Example 5: Calculate the length of the missing sides 300

Example 6: Area What is the area of an equilateral triangle that has a side length of 20in? Leave your answer in simplest radical form.

5-8 Classwork (not graded) Workbook pg 230 ALL Rationalize the denominator if necessary. × 2 Long Leg Short Leg Hypotenuse × 3 ÷ 3 ÷ 2 Leg Hypotenuse × 2 ÷ 2

Honors: 5-8 Assignments Primary Assignment: join.quizizz.com Codes: Period 1: Period 5: Period 6: Secondary Assignment: Workbook pg 231 #1 – 6 Workbook pg 232 #1, 2, 5, 6

Standard: 5-8 Assignments Primary Assignment: join.quizizz.com Codes: Period 2: Period 4: Period 7: Secondary Assignment: Workbook pg 231 #1 – 6 Workbook pg 232 #2, 5, 6