Question
Based on the given information, what can you conclude, and why?
Given: The measure of angle P equals the measure of angle T.; P R equals T R
Segment Q T intersects segment P S at point R. Points Q and P on the left are joined to form segment Q P. Points S and T on the right are joined to form segment S T. The entire figure is two triangles joined at point R.Point Q is in the upper left and Point T is in the lower right of the figure. A segment connects Q and T.
Point S is in the upper right and Point P is in the lower left of the figure. A segment connects P and S.
Segment Q T intersects Segment S P at point R. A segment is drawn between Q and P. A segment is drawn between S and T.
(1 point)
Responses
Triangle Q R P is congruent to triangle T R Sby SAS.
Image with alt text: Triangle Q R P is congruent to triangle T R S by SAS.
Triangle Q R P is congruent to triangle S R Tby SSS.
Image with alt text: Triangle Q R P is congruent to triangle S R T by SSS.
Triangle Q R P is congruent to triangle S R Tby ASA.
Image with alt text: Triangle Q R P is congruent to triangle S R T by ASA.
Triangle Q R P is congruent to triangle S T Rby ASA.
Based on the given information, you can conclude that Triangle QRP is congruent to Triangle STR by ASA (Angle-Side-Angle) theorem. This is because Angle P is equal to Angle T, PR is equal to TR, and Segment PT serves as the common side between the two triangles.
Based on the given information, we can conclude that Triangle QRP is congruent to Triangle STR by SAS (Side-Angle-Side). This is because the measure of angle P equals the measure of angle T, and PR equals TR.
To determine which conclusion is correct, we need to analyze the given information.
We are given that:
1. The measure of angle P equals the measure of angle T.
2. PR equals TR.
3. Segment QT intersects segment PS at point R.
Based on this information, we can conclude that Triangle QRP is congruent to triangle STR by SAS (Side-Angle-Side).
Here's why:
1. The measure of angle P equals the measure of angle T (given).
2. PR equals TR (given).
3. They share a common side, which is segment PR (common side).
4. Therefore, Triangle QRP and triangle STR have two congruent sides (PR and TR) and a congruent angle (angle P equals angle T).
Hence, the correct conclusion is "Triangle Q R P is congruent to triangle T R S by SAS".