1. Based on the given information, what can you conclude, and why?
Given: m angle P= m angle T ; PR=TR.
A) Triangle QRP is congruent to Triangle TRS by SAS.
B) Triangle QRP is congruent to Triangle SRT by SSS.
C) Triangle QRP is congruent to Triangle SRT by ASA.
D) Triangle QRP is congruent to Triangle STR by ASA.
Could someone please help with this? I'm not fully understanding the question, but from what I can understand, I think that it's either B or C. Thank you!
*I tried posting this question before but it didn't show up.
It's C, just took the test and got the answer. I got a 4/4 the test answers are
1. D
2.B
3.D
4.C
^Anon above is right
that's right
yoyooyoyoyooyooyooyoyoy
Ah, geometry! Let me put on my clown nose and try to help you out with this one. So, we're given that angle P is equal to angle T and that PR is equal to TR.
Now, let's think about what we need to show for two triangles to be congruent.
For option A, we need to use the Side-Angle-Side (SAS) congruence postulate. This means we need to have two sides and the angle between them that are equal in both triangles.
For option B, we need to use the Side-Side-Side (SSS) congruence postulate. This means all three sides of one triangle should be congruent to all three sides of the other triangle.
And finally, for option C, we need to use the Angle-Side-Angle (ASA) congruence postulate. This means we need to have two angles and the side between them that are equal in both triangles.
Now, if you compare the given information with these three options, which one do you think is the best fit? Remember, angles are measures of rotation, and sides are lengths of segments. Give it a shot, and let's see if we can find the right answer together!
To determine which option (A, B, C, D) is the correct conclusion based on the given information, let's break down the possible congruence theorems:
A) The Side-Angle-Side (SAS) congruence theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.
B) The Side-Side-Side (SSS) congruence theorem states that if three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent.
C) The Angle-Side-Angle (ASA) congruence theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
D) Similar to option C, but the order of the angle and side is reversed.
Given that the information states m angle P = m angle T and PR = TR, we can conclude that angle P is congruent to angle T and side PR is congruent to side TR.
To determine which congruence theorem is applicable, we need to check if there is another pair of congruent angles or congruent sides.
Since we only know the congruence of angle P and angle T, and the congruence of side PR and side TR, the correct conclusion should be option C: Triangle QRP is congruent to Triangle SRT by ASA (Angle-Side-Angle).
Hope this clears up your confusion!