name geometry unit 3 note packet similar triangles · name _____ geometry unit 3 note packet...
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NAME ______________________________ GEOMETRY
UNIT 3 NOTE PACKET
SIMILAR TRIANGLES
Date Page(s) Topic Homework 10/10
2&3 Definition of similar triangles
Finding angles and sides for simple similar triangles
Pg 369 #35,38,39 Pg 375 #1-6,10,11
10/11
4 Solve for x in similar triangles Pg 376 # 13,21,23-28,32,33
10/15
5 Discover ratio for sides, perimeter, area of similar triangles
Pg 555 #1-3,5
10/16
Review all Quiz
No homework
10/17
6 Prove triangles are similar Worksheet on proof/problem attic
10/18
7 Side Splitter Theorem (redrawing into two similar triangles)
No homework
10/21 8 Mid-segment Theorem (redraw triangles and come to a conclusion)
Worksheet with side splitter & mid-segment
10/22 9 Quiz Geometric mean
Pg. 394 # 1-8
10/23 10 & 11 Similarity in right triangles(Leg) No homework 10/24 12 Similarity in right triangles (Alt) Pg. 394 # 9-14
10/28 Similarity in right triangles (both ) Pg. 394 #15-18,34
10/29 Review Finish Review Packet/ Ticket-In
10/30 TEST No homework
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Vocabulary Unit 3
Term Definition Picture
Similar Triangle
Ratio
Proportion
Congruent Angles
3
Complete the congruence and proportion statements in the diagram below:
1.)∡B≅ _____ 2.) ∡E ≅ _______ 3.) ∡D≅ _______
4.) 5.) 6.)
7.) Fill in all of the missing sides and angles in the isosceles trapezoids below:
A
B
C
D E
F
I
H
G
ABCDE~FGHIE
R O
K C
H A
R D
ROCK~HARD 6 9
15
12
60
4
SOLVING FOR X IN SIMILAR TRIANGLES
State whether or not the polygons are similar. If they are then give the similarity ratio:
1.) 2.)
Find the missing variables and state the similarity ratio:
3.) NMQP~SRUT 4.) ∆ABC~∆DEF
5.)As shown in the diagram below, , , , , and .
What is the length of ?
6.) In the diagram below, , , , , and .
Determine the length of .
5 in.
A
C E
D
F B
5
40
70
10 x y
4 z
RATIO FOR SIDES, PERIMETER AND AREA
OF SIMILAR TRIANGLES
Use the following triangles to determine the relationship between ratios of sides, perimeters and areas in the
given similar triangles.
What do you notice?
What do you notice?
10 6
8
12
20
15 25
5
3
15
9
4
6
PROVING TRIANGLES ARE SIMILAR
Fill in the missing ANGLES
If two angles in a triangle are congruent then the third angles _________________________________.
Therefore you can prove that triangles are similar by: ___________________________.
1.) In the diagram below of , Q is a point on , S is a point on , is drawn, and .
Prove: ΔRPT~ΔRSQ
2.) In the diagram of and below, and intersect at C, and AB∥DE.
Prove: ΔABC~ΔDEC
70
70
65
65
7
SIDE SPLITTER THEOREM
2.) What about this?
x
10
If a line is parallel to one side of a triangle then we know that the _________________ angles are ______ and
since the two triangles share an _________ we know that the ___________ are ________ b/c of_________.
Since the parallel line intersects the other two sides at the same rate the sides (not the parallel lines)___________
into equal ___________ .
Corollary to Side-Splitter Theorem
If three parallel lines intersect two transversals, then _______________________________________
_________________________________________________________________________________.
6
8
1.)
9
GOMETRIC MEAN
THINKING AHEAD:
Fill in the missing angles: In all the triangles if AC is an altitude in right triangle BAP
30
B
C P
A
10
SETTING UP PROPORTIONS USING ALTITUDE
A
Th
e
alti
tud
e
to
the
hy
pot
en
use
of
a
rig
ht
tria
ngl
e
divi
des
the
tria
ngl
e
int
o
tw
o
tria
__________________ = ___________________
The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the length of the
segments of the hypotenuse.
B
C
P
Altitude
Part of
hypotenuse
Part of
hypotenuse
11
3.)
O
G
C
H
A
X
12
SETTING UP PROPORTIONS USING LEGS
2.)
what is the length of ? What is the length of ?
3.) In the diagram below, the length of the legs and of right triangle ABC are 6 cm and 8 cm,
respectively. Altitude is drawn to the hypotenuse of . What is the length of to the nearest tenth
of a centimeter?
AND