Vocabulary
Similar Polygons
Proving Triangles Similar
Proving Quadrilaterals
Mixed Theorems
100
Any parallelogram with 4 right angles.
Square or Rectangle
100
The polygons are similar. Find the value of x.
x = 12
100
Determine whether the triangles are similar. If they are, write a similarity statement. SHOW WORK.
no; m∠R = 60°
100
Name all the possible quadrilaterals that the statement is true for:
Diagonals are congruent
Rectangle & Square
100
Determine whether △JKL or △RST is similar to △ABC.
△RST
200
Which statement is true? A) A trapezoid has 2 pairs of parallel sides. B) A parallelogram has 2 pairs of parallel sides. C) A Square has only 2 right angles. D) A rectangle has only 5 sides.
B) A parallelogram has 2 pairs of parallel sides.
200
The polygons are similar. Find the value of x.
x = 11
200
Determine whether the triangles are similar. If they are, write a similarity statement. SHOW WORK.
yes; ∠H ≅ ∠J and ∠F ≅ ∠K, so △FGH ∼ △KLJ.
200
In the diagram VWXY is a parallelogram, complete each statement
<VYX is supplementary to ? and ?.
<VYX is supplementary to <WVY & <WXY
200
x = 12
300
A quadrilateral with 1 pair of parallel sides, 1 pair of equal sides, and no right angles
Isosceles Trapezoid
300
The polygons are similar. Find the values of x and y.
x = 7.5, y = 166
300
Show that the two triangles are similar.
∠N ≅ ∠Z and ∠MYN ≅ ∠XYZ (vertical angles), so △MYN ∼ △XYZ.
300
Name all the possible quadrilaterals that the statement is true for:
Opposite sides are parallel
Parallelogram, Rhombus, Rectangle, & Square
300
DE || AC
Find AB
AB= 44.8
400
This is a correct similarity statement for these two triangles.
What is
△JGH~△LKM?
400
The polygons are similar. Find the values of x and y.
x = 35.25, y = 20.25
400
Show that the two triangles are similar.
∠Q ≅ ∠MPN (corresponding angles) and ∠N ≅ ∠N, so △LNQ ∼ △MNP.
400
Prove that the following points represent the vertices of a rectangle:
M: (3, -4) , N: (3, 7) , P: (-5 , -4) , Q: (-5 , 7 )
slope of MN & PQ =undefined
slope of NQ & MP =0
measure of MN & PQ = 11 units
measure of NQ & MP = 8 units
400
In Exercises 5 and 6, fi nd the value of x that makes △DEF ∼ △XYZ.
x = 6
500
A quadrilateral with 2 pairs of parallel sides and 4 equal sides, but no right angles
Rhombus
500
Autumn is 1.25 meters tall. At 10 a.m., she measures the length of a tree's shadow to be 22.85 meters. She stands 18.3 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
The tree is 6.28 m tall.
500
Sow that the triangles are similar and write a similarity statement. Explain our reasoning.
∠ACB ≅ ∠DCE and CE/CB = DC/AC, so △ABC ∼ △DEC.
500
Prove that the following points represent the vertices of a parallelogram:
A: ( 2 , 4 ) , B: ( 4 , -3 ) , C: ( 9 , -6 ) , D: ( 7 , 1 )
slope of AB & CD = -7/2
slope of BC & AD = -3/5
measure of AB & CD = root 53
measure of BC & AD = root 34
500
How tall is the person? (feet, inches)
4 feet 4 inches