7.1
write a simplified ratio: a bonsai tree is 18 in wide and 2 ft tall
3:4
what is a scale factor
ratio of corresponding side measurements of 2 similar figures
name the three ways to prove triangles similar
AA similarity, SAS similarity, SSS similarity
what is an altitude
segment that intersects the vertex and is perpendicular to the opposite side
side-splitter theorem
if a line parallel to one side of a triangle intersects the other two sides, then it divides those sides proportionally
write a ratio: width of a canoe- 28 in, length of a canoe- 12 ft, 2 in
14:73
if rectangle ABCD has length AB=10 and AD=15, and rectangle EFGH has length EF=15 and EH=20, are the rectangles similar?
no, the scale factor would be 2/3 to 3/4
if triangle ABC has lengths AB=9, BC=6, AC=6, and triangle EFG lengths EF=12, FG=8, EG=8, are they similar
yes, SSS similarity
which theorem relates to altitudes of right triangles (no name)
the altitude to the hypotenuse divides the right triangle into two triangles that are similar to each other and the original triangle
find a:
a/a+4 = 12/8
a=8
the lengths of a triangle are 4:7:9, the perimeter is 60. what are the side lengths
12:21:27
if a poster is 6 in high by 12 in wide, and it can go in a 3 ft by 4.5 ft space, how large can the poster be?
33 in x 55 in
given: triangle ABC and PBM, MP is parallel to AC
prove: triangle ABC and PBM are similar
angle CBA = PBM -VAT
angle CAB = MPB -AIAT
triangle ABC is similar to PBM -AA similarity
find the geometric mean of 4 and 18
6 square root 2
triangle-angle-bisector theorem
if a ray bisects an angle of a triangle, it divides the opposite sides into two segments that are proportional to the other 2 sides
9/2 = x/14
x=63
AD=9, AB=5, BC=7.5
ED=6, EF=y, FG=x
if ABCD was similar to EFGH, find x and y
y= 10/3
x=5
1st corollary to altitude theorem/ first formula
length of the altitude equals geometric mean of segment pieces of hypotenuse
segment 1/altitude = altitude/segment 2
given: triangle DOG with midpoint of DO- H, and OG - T, HT is parallel to DG
prove: DH/OH = GT/OT
ask Maggie for picture on phone im not typing all that
name all three properties of proportions
1. a/b = c/d is equivalent to b/a=d/c
2. a/b = c/d is equivalent to a/c = b/d
3. a/b = c/d is equivalent to a+b/b = c+d/d
darius wants to know how high the cliff he is climbing is. he walks 34 feet back, places the mirror down, and walks another 6 feet back. he is 5.5 feet tall. what is the height of the cliff?
31.16 repeating
2nd corollary to altitude theorem/ 2nd formula
altitude separates the hypotenuse so that the length of each leg of the triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to the leg
hypotenuse/leg = leg/adjacent segment
if a ray bisects a triangle, the opposite sides are split from left to right into segments of 9.6 and 16. the other two sides are y and 24
find y
y=14.4