Question
Deepak is measuring sides and angles of triangle FGH to determine whether it is congruent to triangle MNP shown below.
Triangle M N P. Side P N is 26.7 centimeters, side M N is 18.3 centimeters, and side P M is 14.2 centimeters. Angle P is 40 degrees, angle N is 30 degrees, and angle M is 110 degrees.
Deepak found that Angle G has a measure of 50° and Segment F H is 18.3 centimeters long. Does he need to continue measuring sides and angles of triangle FGH and why?
No, he knows that the triangles are congruent because there are corresponding sides and angles that are congruent.
No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.
Yes, he must verify that the other two side lengths and the other two angle measures are the same as those found in triangle MNP.
Yes, he must only verify that the other two angle measures are the same as those found in triangle MNP.
Triangle M N P. Side P N is 26.7 centimeters, side M N is 18.3 centimeters, and side P M is 14.2 centimeters. Angle P is 40 degrees, angle N is 30 degrees, and angle M is 110 degrees.
Deepak found that Angle G has a measure of 50° and Segment F H is 18.3 centimeters long. Does he need to continue measuring sides and angles of triangle FGH and why?
No, he knows that the triangles are congruent because there are corresponding sides and angles that are congruent.
No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.
Yes, he must verify that the other two side lengths and the other two angle measures are the same as those found in triangle MNP.
Yes, he must only verify that the other two angle measures are the same as those found in triangle MNP.
Answers
GPT-4o mini
To determine whether triangle FGH is congruent to triangle MNP, Deepak needs to compare the sides and angles of both triangles based on the criteria for triangle congruence.
Given that:
- Angle G is 50°,
- Segment FH is 18.3 cm,
- The angles of triangle MNP are: Angle P = 40°, Angle N = 30°, Angle M = 110°.
From the information provided, we can see that angle G (50°) does not correspond to any angle in triangle MNP, indicating that there might be a discrepancy in congruence.
The correct answer is:
**No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.**
This is because he already has information that indicates a mismatch in the angles, and thus, he does not need to continue measuring further to determine non-congruence.
Given that:
- Angle G is 50°,
- Segment FH is 18.3 cm,
- The angles of triangle MNP are: Angle P = 40°, Angle N = 30°, Angle M = 110°.
From the information provided, we can see that angle G (50°) does not correspond to any angle in triangle MNP, indicating that there might be a discrepancy in congruence.
The correct answer is:
**No, he knows that the triangles are not congruent because those measurements are not equal to the corresponding parts of triangle MNP.**
This is because he already has information that indicates a mismatch in the angles, and thus, he does not need to continue measuring further to determine non-congruence.