# What are the missing parts that correctly complete the proof? Given: Point A is on the perpendicular bisector of segment P Q. Prove: Point A is equidistant from the endpoints of segment P Q. Image: A horizontal line segment P Q. A midpoint is drawn on segment P Q labeled as X. A vertical line X A is drawn. A is above the horizontal line. The angle A X Q is labeled a right angle. The line segments P X and Q X are labeled with a single tick mark. A dotted line is used to connect point P with point A. Another dotted line is used to connect point Q with point A. Drag the answers into the boxes to correctly complete the proof. Statement Reason 1. Point A is on the perpendicular bisector of PQ¯¯¯¯¯. Given 2. PX¯¯¯¯¯≅QX¯¯¯¯¯¯ Response area 3. ∠AXP and ∠AXQ are right angles. Response area 4. Response area All right angles are congruent. 5. AX¯¯¯¯¯≅AX¯¯¯¯¯ Reflexive Property of Congruence 6. △AXP≅△AXQ Response area 7. ​ AP¯¯¯¯¯≅AQ¯¯¯¯¯ ​ Response area 8. Point A is equidistant from the endpoints of PQ¯¯¯¯¯. Definition of equidistant Look below me

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## Question:

Quincy folds a piece of cardboard to make the three sides of a triangular prism open at top

and bottom. The triangular prism and the piece of cardboard that he used are shown below.
What is the area of the piece of cardboard? The missing parts that complete the proof are;

2) Definition of a bisector.

3) Perpendicular Definition.

4) ∠AXP ≅ ∠AXQ

6) SAS Congruence Theorem.

7) Corresponding sides of 2 congruent triangles are congruent.

• We are given that;

Point A is the perpendicular bisector of PQ

Point A is equidistant from the endpoints of PQ.

• 2) We are told that PX = QX; Since A bisects PQ at X, it means it divides it into 2 equal parts. Thus, this id true because it corresponds with the definition of a bisector.
• 3.  ∠AXP and ∠AXQ are right angles; Since perpendicular means right angle or 90°, we can say that this statement is true because it corresponds with the definition of perpendicular.
• 4. All right angles are congruent; This simply means they are equal. Thus, the two right angles here ∠AXP and ∠AXQ are congruent. We can write this with congruency symbol as; ∠AXP ≅ ∠AXQ
• 6. △AXP≅△AXQ; This means that △AXP is congruent to △AXQ. From the diagram, we can see that AP = AQ and that QX = PX and that ∠AXP = ∠AXQ. This means 2 corresponding sides and one corresponding angle are equal and the congruence theorem this depicts is SAS Congruence Theorem.
• 7. AP = AQ; This is true because we are told A is equidistant from both P and Q. Also, from the SAS congruency theorem, we can say that the corresponding sides AP and AQ are congruent.
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From the answer and question examples above, hopefully, they may assist the student solve the question they had been looking for and notice of the whole thing declared in the answer above. You would possibly then have a discussion with your classmate and continue the school learning by studying the question jointly.