Question

100 POINTS!!!! PLZ HELP ME, I AM AN IDIOT!

In the figure, k>0.

(a) Is ΔABC similar to ΔPQR? Support your answer with a theorem or postulate.

(b) How does the area of ΔPQR compare tot he area of ΔABC? Justify your answer.

Answer 1

Answer and Step-by-step explanation:

For question A)

ABC is similar to PQR because of the AA similarity postulate. This postulate states that if any two angles in a triangle are congruent to the other two angles in a triangle, then the triangles are similar.

For question B)

The area would be k times more than the area of ABC.

The area of a triangle is bh/2, or base times height, divided by 2.

And since they both have 4, the one with the k will be k times greater.

Hopefully this helps!!

#teamtrees #WAP (Water And Plant)

Answer 2

• (a) yes
• (b) Area of ΔPQR is k² times greater

Explanation:

(a) As per the diagram, the triangles are similar.

• ∠B ≅ ∠Q and ∠C ≅ ∠R

ΔABC ~ ΔPQR as per AA similarity postulate (two congruent angles)

(b) The area is the product of two dimensions. Area of ΔABC

• A = 1/2bh

Since each side of ΔPQR is k times greater than corresponding sides of ΔABC, the base and height will be both k times greater.

So the area of ΔPQR will be:

• A = 1/2bkhk = 1/2bh*k²

The area of PQR is k² times greater than the area of ΔABC