HG_Day 2_10.1_Similar Right Triangles.notebook

What does rationalizing the denominator mean?

January 08, 2015

HG_Day 2_10.1_Similar Right Triangles.notebook

January 08, 2015

10.1 ­ Similar Right Triangles

Altitude -

Similar Right Triangles Theorem

C A

B

D

T W

V

U

a. Identify the 3 similar triangles

b. Which side in ΔTUV corresponds to UW in ΔVUW? c. TU = VU VU ?

If the altitude is drawn to the  hypotenuse of a right triangle,  then the two triangles formed  are similar to the original  triangle and to each other. 

HG_Day 2_10.1_Similar Right Triangles.notebook

January 08, 2015

e t i r W   k c

i u Q

What similarity theorem(s) (AA, SSS, SAS) proves that the 3  right triangles above are similar? Write a paragraph proof in  less than 60 words. 

HG_Day 2_10.1_Similar Right Triangles.notebook

January 08, 2015

Homework Questions?

HG_Day 2_10.1_Similar Right Triangles.notebook

The Geometric Mean - Algebraically

If  a  =   x     x       b  , then x is called the          geometric mean of a and b.

Find the geometric mean of 2 and 18.

January 08, 2015

HG_Day 2_10.1_Similar Right Triangles.notebook Geometric Mean Theorems If the altitude is drawn to the hypotenuse of a right triangle, then the length of the altitude is the geometric mean of the lengths of the segments of the hypotenuse.

x a

b

Find the length of x.

4 10

x

If the altitude is drawn to the hypotenuse of a right triangle, then the length of each leg is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse adjacent to that leg.

x a

b

x b

a

Find the value of x.

x 3

9

January 08, 2015

HG_Day 2_10.1_Similar Right Triangles.notebook

January 08, 2015

RQS  ~   TQR ~     TRS

20 8 6 6√5 7.2 9 4√10 4√3

HG_Day 2_10.1_Similar Right Triangles.notebook

pair-share Turn to the person next to you and tell  them two things that you learned today.  You and your partner cannot share the  same two ideas. Be specific and be  prepared to share out.  

January 08, 2015