Question

Are triangles the congruent? Write the congruency statement.

Answer 1

Answer:

Yes. but under the next condition m∠Q ≅ m∠T

Step-by-step explanation:

If the circular arc label of the angles ∠Q and ∠T means that they are congruent (equal) or m∠Q ≅ m∠T, in that case we can prove that  ΔPQR is congruent with ΔSTU or ΔPQR≅ΔSTU.

We need three elements to form congruency statement.

1.  Sides PQ ≅ ST = 4 ft

2. Angles m∠Q ≅ m∠T

2. Sides QR ≅ TU = 6 ft

Based on the SAS statement ( Side-Angle-Side) we prove that:

ΔPQR ≅ ΔSTU.

If they are congruent, every corresponding elements are congruent:

Sides PR = SU => 3y - 2 = y + 4 => 3y - y = 4 + 2  => 2y = 6 => y = 6/2 = 3

y = 3  => PR = 3 · 3 - 2 = 9 - 2 = 7  =>  PR = 7 ft

Perimeter of ΔPQR is

P = PQ + QR + PR = 4 + 6 + 7 = 17 ft

P = 17 ft

God with you!!!