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Congruent Sides: JK≅ LM, JM≅ KL
Congruent Angles: m∠ KJM≅ m∠ KLM, m∠ JML≅ m∠ JKL
Reasoning: See solution for the explanation.
ST=3feet
m∠ QTS=123^(∘)
m∠ TQR=57^(∘)
m∠ TSR=57^(∘)
Reasoning: See solution for the explanation.
The Parallelogram Opposite Sides Theorem states that the opposite sides of a parallelogram are congruent.
We have two pairs of congruent sides, JK≅ LM and JM≅ KL.
The Parallelogram Opposite Angles Theorem states that the opposite angles of a parallelogram are congruent.
We have two pairs of congruent angles, m∠ KJM≅ m∠ KLM and m∠ JML≅ m∠ JKL.
We know that QT∥RS and QT=RS. In other words, sides QT and RS of the quadrilateral are parallel and congruent.
We can see that QT and RS are opposite sides of quadrilateral QRST. Since they are also parallel and congruent, by the Opposite Sides Parallel and Congruent Theorem QRST is a parallelogram.
Recall that by the Parallelogram Opposite Sides Theorem the opposite sides of a parallelogram are congruent, which means that they have the same measure.
ST=QR QR= 3ft ⇒ ST= 3ft The side ST is 3feet long.
Recall that by the Parallelogram Opposite Angles Theorem the opposite angles of a parallelogram are congruent.
The opposite angles ∠ QTS and ∠ QRS are congruent, ∠ QTS≅∠ QRS. This means that m∠ QTS=m∠ QRS. We also know that m∠ QRS=123^(∘). m∠ QTS=m∠ QRS m∠ QRS=123^(∘) ⇓ m∠ QTS=123^(∘) The angle ∠ QTS measures 123^(∘).
m∠ QRS= 123^(∘)
LHS-123^(∘)=RHS-123^(∘)