if a triangle is divided into two smaller triangles by an altitude and all three triangles are similar, what theorem could this be used to prove?
a. sas criterion
b. hl criterion
c. sss criterion
d. pythagorean theorem

which criterion requires two angles of one triangle to be congruent to two angles of another triangle for the triangles to be similar?
a. sss
b. aa
c. asa
d. sas

in $ \triangle xyz $, the angle bisector of $ \angle yxz $ intersects $ yz $ at $ p $. if $ xy = 8 $, $ xz = 12, yp = 4 $, and $ pz = 6 $, verify the angle bisector theorem.
a. $ \frac { y p } { p z } = 0.6, \frac { x y } { x z } = 1.25 $
b. $ \frac { y p } { p z } = 0.75, \frac { x y } { x z } = 0.75 $
c. $ \frac { y p } { p z } = 0.67, \frac { x y } { x z } = 0.67 $
d. $ \frac { y p } { p z } = 1, \frac { x y } { x z } = 1.5 $

in $ \triangle a b c, d $ and $ e $ are midpoints of $ a b $ and $ a c $. if $ a b = 12 $ and $ a c = 16 $, what is the length of $ d e $?
a. 6
b. 9
c. 10
d. 8

in triangle $ a b c $, if $ a b = 10 $ units, $ b c = 8 $ units, and $ a c = 6 $ units, what type of triangle is triangle $ a b c $?
a. isosceles
b. right
c. scalene
d. equilateral

in $ \triangle x y z, \angle x y z = 90 ^ { \circ } $, and $ y w $ is the altitude to $ x z $. if $ x w = 9 $ and $ w z = 16 $, what is the value of $ x z $?
a. 30
b. 20
c. 35
d. 25

in $ \triangle p q r, \angle p q r = 90 ^ { \circ } $, and $ q s $ is the altitude to $ p r $. if $ p q = 6 $ and $ q r = 8 $, what is the length of $ q s $ if $ p r = 10 $?

Question

if a triangle is divided into two smaller triangles by an altitude and all three triangles are similar, what theorem could this be used to prove?
 a. sas criterion
 b. hl criterion
 c. sss criterion
 d. pythagorean theorem

which criterion requires two angles of one triangle to be congruent to two angles of another triangle for the triangles to be similar?
 a. sss
 b. aa
 c. asa
 d. sas

in $ \triangle xyz $, the angle bisector of $ \angle yxz $ intersects $ yz $ at $ p $. if $ xy = 8 $, $ xz = 12, yp = 4 $, and $ pz = 6 $, verify the angle bisector theorem.
 a. $ \frac { y p } { p z } = 0.6, \frac { x y } { x z } = 1.25 $
 b. $ \frac { y p } { p z } = 0.75, \frac { x y } { x z } = 0.75 $
 c. $ \frac { y p } { p z } = 0.67, \frac { x y } { x z } = 0.67 $
 d. $ \frac { y p } { p z } = 1, \frac { x y } { x z } = 1.5 $

in $ \triangle a b c, d $ and $ e $ are midpoints of $ a b $ and $ a c $. if $ a b = 12 $ and $ a c = 16 $, what is the length of $ d e $?
 a. 6
 b. 9
 c. 10
 d. 8

in triangle $ a b c $, if $ a b = 10 $ units, $ b c = 8 $ units, and $ a c = 6 $ units, what type of triangle is triangle $ a b c $?
 a. isosceles
 b. right
 c. scalene
 d. equilateral

in $ \triangle x y z, \angle x y z = 90 ^ { \circ } $, and $ y w $ is the altitude to $ x z $. if $ x w = 9 $ and $ w z = 16 $, what is the value of $ x z $?
 a. 30
 b. 20
 c. 35
 d. 25

in $ \triangle p q r, \angle p q r = 90 ^ { \circ } $, and $ q s $ is the altitude to $ p r $. if $ p q = 6 $ and $ q r = 8 $, what is the length of $ q s $ if $ p r = 10 $?

Accepted Answer

# Explanation:
## Step1: Calculate $ \frac{YP}{PZ} $
Given $ YP = 4 $ and $ PZ = 6 $, then $ \frac{YP}{PZ}=\frac{4}{6}=\frac{2}{3}\approx0.67 $
## Step2: Calculate $ \frac{XY}{XZ} $
Given $ XY = 8 $ and $ XZ = 12 $, then $ \frac{XY}{XZ}=\frac{8}{12}=\frac{2}{3}\approx0.67 $

# Answer:
c. $ \frac{YP}{PZ}=0.67,\frac{XY}{XZ}=0.67 $

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate \( \frac{YP}{PZ} \)

Step2: Calculate \( \frac{XY}{XZ} \)

Answer: