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?
o a. sas criterion
o b. hl criterion
o c. sss criterion
o 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?
o a. sss
o b. aa
o c. asa
o d. sas
in △xyz, the angle bisector of ∠yxz intersects yz at p. if xy = 8, xz = 12, yp = 4, and pz = 6, verify the angle bisector theorem.
o a. \\( \frac { y p } { y z } = 0.6, \frac { x y } { x z } = 1.25 \\)
o b. \\( \frac { y p } { y z } = 0.75, \frac { x y } { x z } = 0.75 \\)
o c. \\( \frac { y p } { y z } = 0.07, \frac { x y } { x z } = 0.07 \\)
o d. \\( \frac { y p } { y z } = 1, \frac { x y } { x z } = 1.5 \\)
in △abc, d and e are midpoints of ab and ac. if ab = 12 and ac = 18, what is the length of de?
o a. 6
o b. 9
o c. 10
o d. 8
in triangle abc, if ab = 10 units, bc = 8 units, and ac = 6 units, what type of triangle is triangle abc?
o a. isosceles
o b. right
o c. scalano
o d. equilateral
in △xyz, ∠xyz = 90°, and yw is the altitude to xz. if xw = 9 and wz = 16, what is the value of xz?
o a. 30
o b. 20
o c. 35
o d. 25
in △pqr, ∠pqr = 90°, and qs is the altitude to pr. if pq = 6 and qr = 8, what is the length of qs if pr = 10?

Explanation:

Step1: Calculate the ratio of \( \frac{YP}{PZ} \)

Given \( YP = 4 \) and \( PZ = 6 \), then \( \frac{YP}{PZ}=\frac{4}{6}=\frac{2}{3}\approx0.67 \)

Step2: Calculate the ratio of \( \frac{XY}{XZ} \)

Given \( XY = 8 \) and \( XZ = 12 \), then \( \frac{XY}{XZ}=\frac{8}{12}=\frac{2}{3}\approx0.67 \)

Answer:

c. \( \frac{YP}{PZ}=0.67,\frac{XY}{XZ}=0.67 \)