I need help with this paragraph proof I have no clue what I am doing.

Given: QS bisects angle PQR.
Angle PQS equals 45 degrees.
Prove: PQR is a right triangle.
I really need help, I don't want to fail.

Of course! I'm here to help you. Paragraph proofs can seem intimidating at first, but with some guidance, you'll be able to tackle them with confidence.

To prove that PQR is a right triangle, we can use the information given about the angle bisector and the measure of angle PQS. Here's a step-by-step explanation of how to approach this paragraph proof:

Step 1: Given that QS bisects angle PQR, we know that it divides the angle into two equal parts. This means that angle PQS is congruent to angle SQR.

Step 2: We are also given that angle PQS measures 45 degrees. Since angles PQS and SQR are congruent, both angles have the same measure, which is 45 degrees.

Step 3: Now, recall that for any triangle, the sum of the interior angles is always 180 degrees. Since we have two congruent angles in PQR, let's denote each of them as ∠P and ∠Q.

Step 4: We know that ∠PQS measures 45 degrees and ∠SQP (which is congruent to ∠SQR) also measures 45 degrees. So, we can write an equation to represent the sum of the angles in PQR: ∠P + ∠Q + 45 + 45 = 180.

Step 5: Simplifying the equation, we have ∠P + ∠Q + 90 = 180.

Step 6: To isolate the variable, subtract 90 from both sides of the equation: ∠P + ∠Q = 90.

Step 7: Now, notice that we have a sum of angles equal to 90 degrees. In a triangle, if the sum of two angles is 90 degrees, then the third angle must be a right angle (90 degrees). Therefore, we can conclude that ∠R measures 90 degrees, making triangle PQR a right triangle.

Step 8: Finally, write the conclusion in your paragraph proof, stating that since ∠R measures 90 degrees, triangle PQR is a right triangle.

Remember to use proper mathematical symbols, notation, and terminology when constructing your paragraph proof. Make sure to clearly explain each step, providing logical reasoning and any relevant theorems or properties used along the way. I hope this helps you in completing your proof successfully!

since PQS is half of PQR, PQR is 90 degrees.

QED