Download Similar Triangles - Grade 9 Math Semester 2

Warm up FIND THE UNKNOWN VALUES:
Lesson 3­7: Similar Triangles
40o
25
4
y
xo
10
x
zo
yo
100o
Similar is a mathematical word meaning the same shape.
We say that two triangles, ΔFDE and ΔLMK, are similar if the ratios of corresponding sides are equal.
This equation of three term ratios can also be written in fraction form:
FD DE EF
LM = MK = KL
Corresponding sides are equal
FD : DE : EF = LM : MK : KL
NOTE:
The sides of one triangle must be in the numerator, while the sides of the other triangle are in the denominator.
ΔFDE≈ΔLMK
Prove the two triangles are similar.
In similar triangles, corresponding angles are equal.
∠F = ∠ L
∠D = ∠ M
∠E = ∠ K
IMPORTANT:
If you know two triangles are similar, then their corresponding angles are equal.
Conversely, if two triangles have equal corresponding angles, then the triangles are similar.
SOLUTION:
Sides:
Angles:
BC
AB
∠ A = ∠ D DE = EF =
∠ B = ∠ E
8
∠ C = ∠ F 12 = 69 =
AC
DF
5
7.5
Since corresponding angles are equal, then the triangles are similar. We could also say that since corresponding sides are equal, the triangles are similar. 1
Find the measures of ∠ A, ∠ B, ∠ C.
ΔABC is similar to ΔRPQ. Find the lengths of RP and AC.
SOLUTION:
Sides:
FG = GH
FH
=
BC
AB
AC
3.5
3
=
7
6
=
5.3
10.6
1
2
=
1
2
1
2
=
SOLUTION:
Sides:
8
x
12x = 8(16.8)
x = Therefore: ∠ F = ∠ A
∠ H = ∠ C
∠ G = ∠ B
134.4
12
RP = 11.2
y
12
= 21
16.8
12 = y
21
16.8
16.8y = 12(21)
252
y = 16.8
AC = 15
o
ΔSIP is similar to ΔMAT. Find the lengths of MA and SP
=
8 = 12
16.8
x
Since the ratios of the sides are all equal, the triangles are similar.
Thus, the corresponding angles are equal.
∠ A = 100
o
∠ C = 38
o
∠ B = 42
AC
AB
BC
=
=
RQ
RP
PQ
For the figure below, show that ΔDEF is similar to ΔDGH.
Remember:
If two triangles have equal corresponding angles, then the triangles are similar.
SOLUTION:
Reason
∠ D = ∠ D ∠ E = ∠ G ∠ F = ∠ H common angle
corresponding ∠s
corresponding ∠s
ΔDEF ≈ ΔDGH.
2