7.5 parts of similar triangles 2016 ink.notebook...7.5 parts of similar triangles 2016 ink.notebook...

7.5 parts of similar triangles 2016 ink.notebook

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February 08, 2018

Page 50

7.5 Parts of Similar Triangles

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Lesson Objectives Standards Lesson Notes

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7.5 Parts of Similar Triangles

Lesson Objectives

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Lesson NotesStandards

After this lesson, you should be able to successfully use proportions with special segments in similar triangles.


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Lesson Objectives Standards Lesson NotesG.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

When 2 triangles are similar, corresponding A____________, A___________________, and M_________ are proportional to the corresponding sides.

536

x

56

3x=

If 2 Ë's are ~, the lengths of corresponding altitudes are proportional to the lengths of corresponding sides.

~Ë's have corr. altitudes proportional to corr. sides.

A

BC D

F

GJH

If ËABC ~ ËFGH, then ADFJ

ABFG

=

Altitude: A perpendicular line segment from an angle to the opposite side.


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53

6x

56

3x=

If 2 Ë's are ~, the lengths of corresponding angle bisectors are proportional to the lengths of corresponding sides.

~Ë's have corr. ⁄ bisectors proportional to corr. sides. R

S

Q

T

MP

K L

If ËKLM ~ ËQRS, then LPRT

LMRS

=

Angle Bisector: A line segment that cuts an angle into 2 equal parts.

53 6x

56

3x=

If 2 Ë's are ~, the lengths of corresponding medians are proportional to the lengths of corresponding sides.

~Ë's have corr. medians proportional to corr. sides. A B

C

D

W XZ

Y

If ËABC ~ ËWXY, then CDYZ

ABWX

=

Median: A line segment that connects an angle to midpoint of the opposite side.

1.2.

NAME THE KIND OF SEGMENT SHOWN! Show a proportion and solve for each, finding x.


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3. 4.


5.6.


14

12

12

x


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Triangle Angle Bisector Theorem An angle bisector in a triangle separates the opposite side into two segments that are _______________ to the lengths of the other two sides

7.

8.

Since SU is an ⁄ bisector, RUTU

RSTS

=

10.

9.


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On the Worksheet

a) b)


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February 08, 2018

HOMEWORK

7.5 Practice WS on Parts of Similar Triangles

Find x, and NAME the kind of Segment used….Angle bisector, Median, or Altitude!

__________________, x = _____

1.


__________________, x = _____

2.


__________________, m = _____

3.


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__________________, x = _____

4.

Find the value of each variable.7. m = ______ 8. x = _____


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Find the value of each variable.

9. x = _____ 10. x = _____11. FLAGS An oceanliner is flying two similar triangular flags on a flag pole. The altitude of the larger flag is three times the altitude of the smaller flag. If the measure of a leg on the larger flag is 45 inches, find the measure of the corresponding leg on the smaller flag.

12. TENTS Jana went camping and stayed in a tent shaped like a triangle. In a photo of the tent, the base of the tent is 6 inches and the altitude is 5 inches. The actual base was 12 feet long. What was the height of the actual tent?

How much farther from Hank is point B versus point A?

13. PLAYGROUND The playground at Hank's school has a large right triangle painted in the ground. Hank starts at the right angle corner and walks toward the opposite side along an angle bisector and stops when he gets to the hypotenuse.


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Answers:

x = 16.5

7.5 parts of similar triangles 2016 ink.notebook...7.5 parts of similar triangles 2016 ink.notebook...

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