Answer:
Therefore
1. Vertical Opposite Angle Theorem is used to prove that the triangles are similar.
2. Angle-Angle similarity statement is used.
3. x = 10 unit and y = 7.5 unit.
Step-by-step explanation:
Given:
∠A ≅ ∠E
AB = 8 , DE = 12 , BC = 5 , CE = 15
To Prove:
Δ ABC ~ ΔEDC
To Find :
x = ?
y = ?
Proof:
Vertical Angle Theorem:
The angles opposite each other when two lines cross. They are always equal.
Here vertical opposite angles are,
∴ ∠ACB ≅ ∠ECD
Angle-Angle Similarity :
If in Two triangle Two corresponding angles are congruent then the Triangles are Similar by Angle-Angle Similarity statement.
Now,
In Δ ABC and Δ EDC
∠A ≅ ∠E …………..{ Given }
∠ACB ≅ ∠ECD ……….....{Vertical Opposite Angle Theorem}
Δ ABC ~ Δ EDC ….{Angle-Angle Similarity test}
If two triangles are similar then their sides are in proportion.
On Substituting the given values we get
Therefore,
Therefore
1. Vertical Opposite Angle Theorem is used to prove that the triangles are similar.
2. Angle-Angle similarity statement is used.
3. x = 10 unit and y = 7.5 unit.