Transcript Slide 1

Similar Right Triangles
(MCC9‐12.G.SRT.4; MCC9‐12.G.SRT.5)
•rectangular piece of paper
•ruler
•scissors
•colored pencils
1. How are the two smaller triangles related
to the large triangle?
2. Explain how you would show that the
triangle that includes ∠8 is similar to the
triangle that includes ∠5.
3. Explain how you would show that the
triangle that includes ∠5 is similar to the
triangle that includes ∠2.
4. Write a proportion involving the two legs
of the triangle that includes ∠2 and the
triangle that includes ∠5.
5. Measure the legs in centimeters (to the
nearest tenth) and substitute the values.
6. Cross-multiply. What did you notice?
21.6 cm
17.1 cm
27.9 cm
22.0 cm
7. Could we find the lengths
for the other sides without measuring?
27.9 cm
13.2 cm
35.3 cm
21.6 cm
17.1 cm
17.1 cm
22.0 cm
27.9 cm
21.6 cm
How Can Triangles Be Proven Similar?
Similar ( ) triangles have
congruent ( ) angles and
proportional sides.
Angle – Angle (AA)
A
C
B
91o
C
X
Z
54o
Z
A
10
91o
Y
X
54o
B
Side – Side – Side (SSS)
AB
BC
CA
___
= ___ = ___
XY
YZ
ZX
C
12
Z
6
Y
X
18
C
B
10
91o
C
15
9
A
Side – Angle – Side (SAS)
A
Z
6
9
X
BC
___
=
YZ
91o
Z
CA
___
ZX
15
Y
How Can Triangles Be Proven Similar?
Similar ( ) triangles have
congruent ( ) angles and
proportional sides.
Angle – Angle (AA)
Side – Side – Side (SSS)
B
91o
C
Side – Angle – Side (SAS)
B
10
91o
B
54o
Z
A
10
91o
Y
X
54o
C
12
Z
9
A
6
C
15
A
Y
X
Z
6
18
Dr. Jennifer L. Brown, 2013, Columbus State University, CRMC Summer Workshop
9
X
91o
15
Y
1. Draw a diagonal
from the top left
corner to the lower
right corner.
2. Cut along the
diagonal.
3.
4.
5.
A
D
F
B
E
Label ΔABC (as shown).
Label points D, E, F, & G.
Fold side BC up to meet
point D. (Keep BC ⊥ to AB. )
6. Label point E.
7. Draw segment DE.
8. Repeat step 5 but meet point
F.
G 9. Label point G.
10. Draw segment FG.
C
A
D
F
B
E
11. Measure the length of AC,
AB, and BC (in centimeters
to the nearest tenth).
12. Measure the length of AG,
AF, and FG.
13. Measure the length of AE,
AD, and DE.
G
C