warm up 1)at a certain time of day, a 6 ft man casts a 4 ft shadow. at the same time of day, how...

Warm Up

1) At a certain time of day, a 6 ft man casts a 4 ft shadow. At

the same time of day, how long is the shadow of a tree that is 27 feet tall?

3) ΔABC~ΔDEF. Solve for y.

A

BC

D

EF

10 35

30° 30°

14

Y

2) Find JG J

GE

H

F

4

6

12

x

HW Answers

P 385 #2-16 even2) No; not enough info

given4) Yes, AA ~ Post.

Triangle FHG ~ KHJ6) No8) Yes, SAS ~ Thm.

Triangle NMP ~ NQR10)AA~ Post; 7.5

12)AA~ Post; 12 5/6 14) AA ~ Post; 816)SAS ~ Thm. 12m18) AA~ Post; 15 ft 9in

Due at the end of class.

Practice 7-3 in Workbook p383 #1-12 all• Do problems in your notebook, Write the

question for full credit!! Show all work.

Quiz Tomorrow on Proving Triangles Similar.

Check Answers to Yesterday’s Assignment

• Workbook

Similarity in Right Triangles

Theorem: The altitude to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.

Knowing this theorem, how can you solve for x and y.

x y

4 5

Geometric Mean

• Proportions in which the means are equal.• For any two positive numbers a and b, the

geometric mean of a and b is the positive number x such that: a/x = x/b, then x = _____

• Ex. Find the geometric mean of 4 and 18.

Corollary to previous theorem

Corollary 1: The length of the altitude of the hypotenuse of a right triangle is the geom. Mean of the lengths of the segments of the hypotenuse.

Corollary 2: The altitude of the hyp. Of a right triangle separates the hypotenuse so that the length of each leg of the triangle is the geom. mean of the length of the adjacent hyp. segment and the length of the hyp.

Solve for x and y.

C

6

2 x

y

D BA

Quiz/Assignment

• Complete Quiz, when you are finished, give Ms. Malik your quiz and begin your homework assignment.

• Due Wednesday– P 394 #2-20 even, 34-36– P 401 #1-23 odd (SHOW WORK!!) – Set up all proportions and show work for FULL

credit.

Warm Up

C

y

4 12

x

D BA

HW Questions?

Workbook Practice 7-4

• Whiteboards# 1- 3# 13 - 18

Triangle Proportionality Theorem

• If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

QR QS

RX SY

Q

R S

XY

Example• Find the value of x or y.

2.1.

C

BG

H A5 x

12

4

• You try on white boards.

P

L M

Q

N

5

24

xR

U

S

T

V

14

10

4

y

Find the value of x or y3. 4.

• If three parallel lines intersect two transversals, then the segments intersected on the transversals are proportional.

a c

b d

2 Transversals Proportionality Corollary

a

b

c

d

Practice:1. Find x and y

2. Find the length of LN to the nearest tenth.

C

A

DB

NMLK

4 9

6

12

107.2

On Whiteboards..

4. Find x 3. Find the length

of LM and MN.

C

A

DB

NMLK

10

6

25

2

• If a ray bisects an angle of a triangle, then it divides the opposite side into two segments that are proportional to the other two sides of the triangle.

left left

right right

AC CD

AB DB

A

BC D

Triangle Angle-Bisector Theorem

Practice• Find the value of x.

1.

R

S

V

T

2410

4

2. Find VT

Your turn on wb…3. Find x

4. Find DC

A

B CD

8 14

12

5

Groups

Exit Pass

1.Find JG

J

GE

H

F

4

6

11

x