Warm Up for Section 1.1 (Tuesday, August 7) Simplify: (1). (2). Find the two missing edge lengths in each triangle: (3). (4). (5). 45 o 7

Warm Up for Section 1.1 (Tuesday, August 7) Simplify: (1). (2). Find the two missing edge lengths in each triangle: (3). (4). (5). 45 o 7

Work for Answers to WU, Section 1.1 (1). (2).

Special Right Triangles Section 1.1 Day 2 Essential Question: What is the relationship between the lengths of the edges in a 30°–60°–90° triangle? Standard: MM2G1a, b

Investigation 2: With your partner, complete the following regarding equilateral  ABC where AB =10: Step 1: Label the length of each edge. Step 2: Label the measure of  B and  C. Step 3: Using a straightedge, draw and label altitude. Step 4: Label the length of and. Step 5: Label the measure of  BAD and  CAD. Step 6: Label the measure of  ADC. Step 7: Using the Pythagorean Theorem, find AD.

° 30° 60° a 2 + b 2 = c x 2 = x 2 = = x 2 30° A B C D x

Investigation 2: Note: the two legs of a 30 o -60 o -90 o triangle are NOT equal in measure. The longer leg will always be opposite the ___ o angle. The shorter leg will always be opposite the ___ o angle

Consider the 30 o -60 o -90 o right triangle created from an equilateral triangle pictured at right. (2). The long leg is segment ______ and the short leg is segment _______. (3). Use the Pythagorean Theorem to find RT. RT ST ° 30° R TS

° 30° a 2 + b 2 = c x 2 = x 2 = = x 2 R TS

2x2x x 60° 30° Length of hypotenuse = length of short leg times 2 Length of long leg: length of short leg times Length of short leg: half the length of hypotenuse or the length of the long leg divided by Summary: In a 30 o -60 o -90 o triangle:

Check for Understanding: Find the missing edge lengths for each triangle: Example 4:

Check for Understanding: Find the missing edge lengths for each triangle: Example 5: 60 o 30 o

Check for Understanding: Find the missing edge lengths for each triangle: Example 6:

Check for Understanding: Find the missing edge lengths for each triangle: Example 7: 60 o 30 o

Check for Understanding: Find the missing edge lengths for each triangle: Example 8: 60 o 30 o

Check for Understanding: Find the missing edge lengths for each triangle: Example 9: 60 o 30 o

Application problems: (7). Find the exact area of an equilateral triangle whose edge length is 12 cm. Round your answer to the nearest tenth. Recall: A = ½bh h 60 o A = ½bh A = ½(12) A = A ≈ 62.4 cm 2

Application problems: (8). Find the exact perimeter of square ABDC if FB = 22 meters P = 4s P = 4 P = A F B C D o

60° 30° Formula Sheet: Length of long leg = length short leg ∙ _____ Length of hypotenuse = length short leg ∙ _____ Length of short leg = length long leg ÷ ______ Length of short leg = length hypotenuse ÷ ______

Pythagorean Theorem: a 2 + b 2 = c x 2 = x 2 = 100 x 2 = 51 x = 7 10 x

Triangle Sum Property: Sum of interior  s = _____ 25° 30° x°x° x = 180 o – 25 o – 30 o = 125 o

Linear Pair: x = 180 o – 120 o = 60 o 120° x°x°