L1:Ratios + Proportions
L2:Similar Triangles+Polygons
L3:Proving Triangles Similar
L4:Dilations
Random
100
Q1 = A 65 in tall man wants determine how tall a large tree is. He noticed at a certain time his shadow was 14 in long. When he measured the shadow of the tree he found that it was 48 in long. How tall is the tree? Set up a proportion.
65/14 = x/48
3120= 14x
x≈222.86in
100
write the statement of proportionality for ΔABC and ΔDEF assuming they are similar
m<Am<D
m<Bm<E
m<Cm<F
100
Given: Triangle ABC is a right triangle
AD is an altitude
Prove: Triangle ABC ~ Triangle DAC
Statement Reasons
1) Triangle ABC is a 1) Given
right triangle
2) Angle CAB is a 2)
3) 3)Definition of an altitude
4) 4)All right angles are =
5) Angle C = Angle C 5)
6) Triangle ABC ~ 6)
triangle DAC
2)Definition of a right triangle
3)Angle ADC is a right angle
4)Angle CAB= angle ADC
5) Reflective property
6) AA~
100
if 0<k<1, then the dilation is this
a reduction
100
Point S=(-2,-6)
Point T=(5,8)
Point S lies between T and R. TS:SR =7:3.
What are the coordinates of Point R?
(x-5)(3/10)+x=-2 → -1.5+-3/10x=-5.5
(y-8)(3/10)+y=-6 → -2.4+3/10y=-11.6
R(-5, -12)
200
The perimeter of a rectangle is 40ft. The ratio of the width to the length is 2:3. Find the length and width.
2x
3x
2(2x+3x)=40ft
4x+6x=40ft
10x=40
x=4
3x=length → 3(4)=12ft
2x=width→ 2(4)=8ft
200
The two polygons are similar. Find the values of X and Y
X=69
Y=12.5
200
The triangle is similar. Find x and y.
x=10/3
y=14/3
200
if k>1, then the dilation is this
an enlargement
200
In the diagram PQSR is a square and RSUT~TPQU. Find the value of X. express your answer in exact form and as a decimal approximation. (This number is also known as the Golden Ratio.)
X=
1+1+521.618
300
Find the measures of the angles in each triangle. The ratio of the measures of the angles is 4:5:6
5x
4x6x
4x+5x+6x=180
15x=180
x=12
4(12)=48°
5(12)=60°
6(12)=72°
300
The polygons shown are similar find the ratio (shaded to unshaded) of their perimeters and of their areas.
x
Perimeter 14:11
Area 196:121
300
The ratio of AB to XY is 2:3. In Triangle ABC, m<B =75 degrees, and in Triangle XYZ, m<Y=75 degrees. The ratio to BC to YZ is 2:3.
Name the postulate or theorem that can be used to prove the triangles are similar
SAS~
300
Where does P lie if it is not the center point C?
line CP
300
Given: Triangle ABC is a right triangle
AD is an altitude
Prove: Triangle ABC ~ Triangle DAC
Statement Reasons
1) Triangle ABC is a 1) Given
right triangle
2) Angle CAB is a 2)
3) 3)Definition of an altitude
4) 4)All right angles are =
5) Angle C = Angle C 5) 6) Triangle ABC ~ 6)
2)Definition of a right triangle
3)Angle ADC is a right angle
4)Angle CAB= angle ADC
5) Reflective property
6) AA~
400
Find the point that is ¼ of the way along of ST given S(-2,3) and T(10,-4)
(x2-x1) → 10-(-2)=12 (¼)= 3
(y2-y1) → -4-8=-12(¼)= -3
(-2+3, 8+-3)
(1,5)
400
Use the information about a pair of similar polygons o find all possible values of x
The area of ΔABC is 5
The perimeter of ΔABC is 2
The area of ΔDEF is
x2+9
The perimeter of ΔDEF is x
(2x)25x2+9
=4x2+36=5x2
x=6
400
Find the indicated length
AB=20, AD=16, AC=?
AC=25
400
Identify the dilation, and find its scale factor. Then find the value of the variables
Dilation: Enlargement
Scale factor: 12.5/5
x=20
y=10
400
Find the values of the variables and the scale factor and dilation
Dilation: Reduction
Scale factor: ⅗
x=11.04
500
Point A= -3
Point B=19
Select a point so that the distance from A to it is (3/11) of the distance from A-B
x→ (19+3)=22 (3/11)=6+(-3)=3
y→ (0-0)=0(3/11)=0+0=0
(3,0)
500
The ratio of the areas of two similar triangles is 13:39. What is the ratio of the lengths of corresponding sides?
13:39
1:3
Ratio of areas =
1:√3
500
Find all possible values of x
x=6
500
You are making hand shadows on a wall using a flashlight. You hold your hand 1 foot from the flashlight and 5 feet from the wall. Your hand is parallel to the wall. If the measure from your thumb to ring finger is 6 inches, what will be the distance between them in the shadow?
36 inches or 3 feet