Question

WILL GIVE BRAINLIEST 50 POINTS

Answer 1

These same things are present

• ∆PQR=∆TUV

So

• PQ=TU=12
• <R=<V=75
• <Q=180-(45+75)=60°=<U
• UV=QR=10
• TV=PR=7
• m<T=m<P=45

Answer 2

Answer:

$\sf \overline{PQ}=12$

$\sf \overline{UV}=10$

$\sf \overline{TV}=7$

$\sf m \angle T=45^{\circ}$

$\sf m \angle R=75^{\circ}$

$\sf m \angle Q=60^{\circ}$

$\sf m \angle U=60^{\circ}$

Step-by-step explanation:

≅ sign means that the triangles are congruent, which means they both have the same shape and the same size.

When comparing congruent shapes, inspect the order in which the vertices are given in the statement.

Therefore, if ΔPQR ≅ ΔTUV then:

• $\sf \overline{PQ} \cong \overline{TU}$
• $\sf \overline{QR} \cong \overline{UV}$
• $\sf \overline{PR} \cong \overline{TV}$

Similarly:

• $\sf m \angle P \cong m \angle T$
• $\sf m \angle Q \cong m \angle U$
• $\sf m \angle R \cong m \angle V$

Therefore, from inspection of the triangles:

$\sf \overline{PQ} \cong \overline{TU}=12$

$\sf \overline{UV} \cong \overline{QR}=10$

$\sf \overline{TV} \cong \overline{PR}=7$

$\sf m \angle T \cong m \angle P=45^{\circ}$

$\sf m \angle R \cong m \angle V = 75^{\circ}$

The sum of the interior angles of a triangle is 180°, therefore:

$\sf m \angle Q \cong m \angle U=180^{\circ}-45^{\circ}-75^{\circ}=60^{\circ}$