Question
Tamar is measuring the sides and angles of Triangle T U V to determine whether it is congruent to the triangle below.
For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees.
Which pair of measurements would eliminate the possibility that the triangles are congruent?
Measure of angle T = 25 degrees and Measure of angle U = 45 degrees
Measure of angle T = 110 degrees and Measure of angle V = 25 degrees
Measure of angle T = 25 degrees and TU = 12
Measure of angle T = 110 degrees and UV = 27
For triangle K L M, side K M is 27 millimeters, side L M is 20 millimeters, and side K L is 12 millimeters. Angle K is 45 degrees, angle M is 25 degrees, angle L is 110 degrees.
Which pair of measurements would eliminate the possibility that the triangles are congruent?
Measure of angle T = 25 degrees and Measure of angle U = 45 degrees
Measure of angle T = 110 degrees and Measure of angle V = 25 degrees
Measure of angle T = 25 degrees and TU = 12
Measure of angle T = 110 degrees and UV = 27
Answers
GPT-4o mini
To determine which pair of measurements would eliminate the possibility that triangle T U V is congruent to triangle K L M, we need to analyze the measurements and properties of triangle K L M.
Triangle K L M has the following measurements:
- Side K M = 27 mm
- Side L M = 20 mm
- Side K L = 12 mm
- Angles:
- Angle K = 45 degrees
- Angle L = 110 degrees
- Angle M = 25 degrees
Now let's evaluate each of the provided options to see if they can eliminate the possibility of congruence.
1. **Measure of angle T = 25 degrees and Measure of angle U = 45 degrees:**
- This gives angle T and angle U; angle V could be 110 degrees (angle sum = 180 degrees). These angles match angles K and M in triangle K L M, and thus could be congruent.
2. **Measure of angle T = 110 degrees and Measure of angle V = 25 degrees:**
- This makes angle U = 45 degrees, matching angle K in triangle K L M. Here angle T does not match any angles in triangle K L M, but it could still be tested against sides.
3. **Measure of angle T = 25 degrees and TU = 12:**
- Here you have angle T = 25 degrees that could match angle M, but if side TU = 12 and sides K L and K L are not congruent, the triangles cannot be congruent due to side measures.
4. **Measure of angle T = 110 degrees and UV = 27:**
- With angle T = 110 degrees, this also doesn't match any angle in triangle K L M but the side UV = 27 matches K M. Thus while the triangles might share some congruence in sides, the angles do not line up.
The pair of measurements that would definitively eliminate the possibility that triangles K L M and T U V are congruent is:
- **Measure of angle T = 110 degrees and UV = 27**
This angle is not present in triangle K L M, so the congruence based on angle properties cannot hold here, thereby eliminating the triangles' congruence.
**Final Answer: Measure of angle T = 110 degrees and UV = 27.**
Triangle K L M has the following measurements:
- Side K M = 27 mm
- Side L M = 20 mm
- Side K L = 12 mm
- Angles:
- Angle K = 45 degrees
- Angle L = 110 degrees
- Angle M = 25 degrees
Now let's evaluate each of the provided options to see if they can eliminate the possibility of congruence.
1. **Measure of angle T = 25 degrees and Measure of angle U = 45 degrees:**
- This gives angle T and angle U; angle V could be 110 degrees (angle sum = 180 degrees). These angles match angles K and M in triangle K L M, and thus could be congruent.
2. **Measure of angle T = 110 degrees and Measure of angle V = 25 degrees:**
- This makes angle U = 45 degrees, matching angle K in triangle K L M. Here angle T does not match any angles in triangle K L M, but it could still be tested against sides.
3. **Measure of angle T = 25 degrees and TU = 12:**
- Here you have angle T = 25 degrees that could match angle M, but if side TU = 12 and sides K L and K L are not congruent, the triangles cannot be congruent due to side measures.
4. **Measure of angle T = 110 degrees and UV = 27:**
- With angle T = 110 degrees, this also doesn't match any angle in triangle K L M but the side UV = 27 matches K M. Thus while the triangles might share some congruence in sides, the angles do not line up.
The pair of measurements that would definitively eliminate the possibility that triangles K L M and T U V are congruent is:
- **Measure of angle T = 110 degrees and UV = 27**
This angle is not present in triangle K L M, so the congruence based on angle properties cannot hold here, thereby eliminating the triangles' congruence.
**Final Answer: Measure of angle T = 110 degrees and UV = 27.**