Question

Write a paragraph proof for the following conjecture.

Given: m∠SQR=55°.

m∠PQS=35°.

Prove: △PQR is a right triangle.

Answer 1

See explanation

Explanation:

Given: m∠SQR=55°.

m∠PQS=35°.

Prove: △PQR is a right triangle.

Paragraph proof

`\begin{array}{ccc}&\text{Statement}&\text{Reason}\\ \\1.&m\angle SQR = 55^(\circ)&\text{Given}\\2.&m\angle PQS = 35^(\circ)&\text{Given}\\3. &m\angle SQR+m\angle PQS=m\angle PQR&\text{Angle Addition Postulate}\\4.&m\angle PQR=55^(\circ)+35^(\circ)&\text{Substitution Property of Equality}\\5. & m\angle PQR=90^(\circ)&\text{Simplify}\\6. &\angle PQR\text{ is a }&\text{right angle }\\&\text{right angle}&\text{d}\\ 7.&\triangle PQR&\triangle\text{d} \end{array}`

Here d means definition