Date: 10.1(b) Notes: Right Δ Geometric Means Theorem Lesson Objective: Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse. CCSS: G.SRT 4, 5 You will need: CPR, 4 colored pens
Lesson 1: Right ∆ Similarity Draw right ∆ABC with base AB = 8 cm on a blue line. Using your compass, measure AC to be 4 cm and BC to be 7 cm. A 8 cm B
Lesson 1: Right ∆ Similarity Construct altitude CD _|_ to AB using a compass or a protractor. C A B
Lesson 1: Right ∆ Similarity Trace ∆ACD onto tissue paper. Transform ∆ ∆ACD about ∆ABC and ∆CBD. What do you notice? Draw ∆CBD and ∆ACD facing the same direction as ∆ABC. C A D B
Lesson 1: Right ∆ Similarity Right ∆ Similarity Theorem: The altitude to the hypotenuse of a right ∆ forms 2 ∆s that are similar to each other and to the original ∆. C D A D B C B A C ∆ABC ∆_____ ∆_____
Lesson 2: Geometric Means Corollaries Geometric Means Corollaries: C b a D y D h h x h A x D y B C a B A b C c
Lesson 2: Geometric Means Corollaries Geometric Means Corollaries: C b a D y D h h x h A x D y B C a B A b C c shorter leg = b = h = x h 2 = xy longer leg a y h
Lesson 2: Geometric Means Corollaries Geometric Means Corollaries: C b a D y D h h x h A x D y B C a B A b C c hypotenuse = c = a = b c = b = a b 2 = cx shorter leg b h x b x h
Lesson 2: Geometric Means Corollaries Geometric Means Corollaries: C b a D y D h h x h A x D y B C a B A b C c hypotenuse = c = a = b a 2 = cy longer leg a y h
Lesson 3: Identifying Similar Right ∆s Write a similarity statement comparing the 3 triangles. Draw each triangle separately.
Lesson 3: Identifying Similar Right ∆s Write a similarity statement comparing the 3 triangles. ∆UWV ∆_____ ∆_____
Lesson 4: Finding the Side Lengths in Right Triangles A.Find x, y and z.
Lesson 4: Finding the Side Lengths in Right Triangles B.Complete the equation: x = z z ?
Lesson 5: Measurement Application To estimate the height of Big Tex at the State Fair of Texas, Michael steps away from the statue until his line of sight to the top of the statue and his line of sight in the bottom of the statue form a 90° angle. His eyes are 5 ft above the ground and he is standing 15’3” from Big Tex. How tall is Big Tex to the nearest foot?
10.1: Do I Get It? Yes or No 1.Find the geometric mean between 8 and 10 in simplest radical form. 2.Write a similarity statement. ∆TSR ∆ ∆ 3.If PR = 6 and PT = 9, find PS in simplest radical form.
10.1: Do I Get It? Continued 4.
Extra Practice 1.Find u, v and w.