Note: Your teacher will grade your responses to questions 7–10 to ensure you receive proper credit for your answers.
Solve the following.
If trianglePQR congruent to triangleTSR, what are the congruent corresponding parts?
Two triangles are shown with a shared vertex at R. R is on Segment P T. Segments P Q and R Q meet at point Q above P R. Segments R S and T S meet at point S above R T.
(4 points)
The congruent corresponding parts are:
- ∠PQR is congruent to ∠TSR (corresponding angles)
- ∠QRP is congruent to ∠SRT (corresponding angles)
- ∠QPR is congruent to ∠TSR (corresponding angles)
- Segment PQ is congruent to segment TS (corresponding sides)
- Segment QR is congruent to segment SR (corresponding sides)
- Segment PR is congruent to segment TR (shared side)
To determine the congruent corresponding parts of triangle PQR and triangle TSR, we can use the corresponding congruent sides and angles.
According to the given information:
- Segment PQ and Segment TS are congruent (corresponding sides)
- Segment QR and Segment SR are congruent (corresponding sides)
- Angle PQR and Angle TSR are congruent (corresponding angles)
Therefore, the congruent corresponding parts of triangle PQR and triangle TSR are:
- Side PQ is congruent to side TS
- Side QR is congruent to side SR
- Angle PQR is congruent to angle TSR
To determine the congruent corresponding parts of triangles PQR and TSR, we need to compare their corresponding sides and angles.
Corresponding sides:
- PQ and TS are corresponding sides because they are opposite sides of the shared angle at R.
- QR and SR are corresponding sides because they are the sides that connect to the shared vertex R.
- PR and TR are corresponding sides because they are the remaining sides of the triangles.
Corresponding angles:
- ∠Q and ∠S are corresponding angles because they are the angles formed by corresponding sides PQ and TS.
- ∠P and ∠T are corresponding angles because they are the angles formed by corresponding sides PR and TR.
- ∠R is a common angle to both triangles.
So, the congruent corresponding parts of triangles PQR and TSR are:
- Corresponding sides: PQ ≅ TS, QR ≅ SR, and PR ≅ TR.
- Corresponding angles: ∠Q ≅ ∠S, ∠P ≅ ∠T, and ∠R is a common angle.
Remember, when two triangles are congruent, all their corresponding parts (sides and angles) are congruent as well.