Question

Please help urgent!!

Drag and drop a statement or reason to each box to complete the proof.


Given: PQ¯¯¯¯¯≅PR¯¯¯¯¯


Prove: ∠Q≅∠R

Answer 1

PQ≅PR Given

Draw PM¯¯¯¯¯¯ so that M is the midpoint of QR¯¯¯¯¯. Two points determine a line.

QM≅RM Definition of midpoint

PM≅PM Reflexive property of congruence

PQM≅PR SSS Congruence Postulate

∠Q≅∠R CPCTC

Explanation:

Answer 2

`Q M \cong R M \Rightarrow` definition of midpoint

`\overline{P M} \cong \overline{P M} \Rightarrow` Reflexive property of congruence

`\Delta P Q M \cong \Delta P R M \Rightarrow` SSS congruence postulate

`\angle Q \cong \angle R \Rightarrow` CPCTC theorem

Explanation:

Step 1: Since, M is the midpoint of the line segment QR.

`\overline{Q M} \cong \overline{R M} \Rightarrow` definition of midpoint

Step 2: The reflexive property of congruence states that a line segment or an angle or a shape is always equal to itself.

`\overline{P M} \cong \overline{P M} \Rightarrow` Reflexive property of congruence.

Step 3: The SSS congruence postulate states that if three sides of a triangle are equal to three sides of another triangle, then the two triangles are congruent.

`\Delta P Q M \cong \Delta P R M \Rightarrow` SSS congruence postulate

Step 4: CPCTC theorem states if two triangles are congruent then the sides and angles are also congruent.

`\angle Q \cong \angle R \Rightarrow` CPCTC theorem.