Download Similar Triangles Ratios and Conversions 1.] 27 cats : 24 cats 2.] To

Similar Triangles

Ratios and Conversions
1.]

27 cats : 24 cats
2.]
10 𝑓𝑡
2 𝑖𝑛
To set up 2 separate similar triangles, identify small, medium, and large sides:
ratios to find scale factors
proportions to find missing sides

To set up double similar triangles, identify corresponding sides and bases to solve for missing
sides.
side of small = base of small
entire side of large base of large
5
3
6
x

To find the perimeter:
side of small =
side of large

perimeter of small
perimeter of large
Create equations using extended ratios.
If the ratio of the angles in a triangle are 3 : 5 : 7, find the measure of each angle.
The ratio of the width to length of a rectangle is 5 : 8. If the perimeter of the rectangle is 338
in., find the width and length of the rectangle.
The ratio of the width to length of a rectangle is 3 : 5. If the area of the rectangle is 1215 m2,
find the width and length of the rectangle.

Geometric Mean
1.]

4 and 20
2.]
27 and 3
Proportions
1.]
4
𝑏
=
10
3
2.]
 Parallel Lines Theorems
1.]
2.]
 Angle Bisector Theorem
1.]
2.]
2
𝑎+3
=
4
𝑎
 Proving Triangles Similar:
Similar?
Similar?
Reason?
Reason?
Similarity statement:
Similarity statement:
Similar?
Similar?
Reason?
Reason?
Similarity statement:
Similarity statement:

Similar Polygons:
In the diagram, DEFG ~ PQRS.
1]
Find the scale factor of DEFG to PQRS.
2]
Find the value of x.
3]
Find the value of y.
4]
Find the value of z.

Ratios of Triangles. Solve for the variable given the ratio of the two sides lengths of the
triangle.
1]
AB : BC is 3 : 2
2]
AB : BC is 2 : 5
A
A
4
6
B

1]
C
B
x
Similar Triangle Proofs
Given:
̅̅̅̅
̅̅̅̅
𝐴𝐸 // 𝐵𝐷
Prove:
ΔACE ~ ΔBCD
Statements
Reasons
1.
1. ̅̅̅̅
𝐴𝐸 // ̅̅̅̅
𝐵𝐷
2.
2. Corresponding angles are congruent
3.
3. Reflexive Angle
4.
2]
4. AA~
Given:
Prove:
𝐴𝐵
𝐷𝐸
=
𝐵𝐶
𝐸𝐹
=
𝐴𝐶
𝐷𝐹
ΔABC ~ ΔDEF
Statements
1.
2.
C
x–3
Reasons
1.
2.
3]
Given:
𝐺𝐻
𝐽𝐾
=
𝐻𝐼
𝐾𝐿
H ≅ K
Prove:
ΔGHI ~ ΔJKL
Statements
Reasons
1.
1.
2.
2.
3.
3.
4]
Given:
̅̅̅̅̅ // 𝑂𝑃
̅̅̅̅
𝑀𝑄
Prove:
ΔMNQ ~ ΔPNO
Statements
Reasons
1.
1.
2. QMN ≅ OPN
2.
3.
3. Vertical angles are congruent
4.
4.