Question

PLEASE HELP IF POSSIBLE!!

Answer 1

Answer:

Part 4) AA Similarity Postulate

Part 5)

The congruent angles are

m<ACB=m<CED , m<ABC=m<CDE, m<BAC=m<DCE

The proportional segments are

$\frac{AB}{DC}=\frac{BC}{DE}=\frac{AC}{CE}$

Step-by-step explanation:

Part 4) we know that

If BC is parallel to DE

then

Triangles ABC and CDE are similar by AA Similarity Postulate ( the three interior angles are congruent)

so

m<ACB=m<CED ------> by corresponding angles

m<ABC=m<CDE -----> both angles measure is 90 degrees

m<BAC=m<DCE -----> the sum of the interior angles of a triangle must be equal to 180 degrees

If two figures are similar, then the ratio of its corresponding sides is equal

so

$\frac{AB}{DC}=\frac{BC}{DE}=\frac{AC}{CE}$

substitute the values

$\frac{6}{4}=\frac{8}{DE}=\frac{AC}{CE}$

Find DE

$\frac{6}{4}=\frac{8}{DE}$

$DE=8*4/6=16/3\ units$

In the triangle ABC

Applying Pythagoras Theorem

Find AC

$AC^{2}=AB^{2}+BC^{2}$

$AC^{2}=6^{2}+8^{2}$

$AC^{2}=100$

$AC=10\ units$

Find CE

$\frac{6}{4}=\frac{AC}{CE}$

$\frac{6}{4}=\frac{10}{CE}$

$CE=10*4/6=20/3\ units$