Triangle congruence worksheet with geometric diagrams and handwritten solutions.
A worksheet with ten problems asking to determine if two triangles are congruent, with diagrams and handwritten answers indicating methods like ASA, SSS, and SAS.
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Step-by-step solution for: Write SSS, SAS, ASA, and AAS Congruence if they are congruent ...
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Show Answer Key & Explanations
Step-by-step solution for: Write SSS, SAS, ASA, and AAS Congruence if they are congruent ...
I will solve this problem by examining each pair of triangles and determining if they are congruent based on the markings and the standard triangle congruence postulates (SSS, SAS, ASA, AAS, HL). I'll also check the handwritten answers to see if they are correct.
Let me start by looking closely at each numbered problem.
- First, look closely: The first image shows two triangles sharing a side. One triangle has one tick mark on its base and one tick mark on its left side. The other triangle has one tick mark on its right side. There is a handwritten note "not congruent".
- Next, find information: I need to recall the triangle congruence postulates. For two triangles to be congruent, we need three corresponding parts to be equal (with specific arrangements: SSS, SAS, ASA, AAS, or HL for right triangles).
- Then, review the findings: In this case, we have only one pair of sides marked as equal (the shared side), and no other corresponding sides or angles are marked. Therefore, we cannot conclude that the triangles are congruent. The handwritten answer "not congruent" appears to be correct.
- First, look closely: This image shows two triangles with a common vertex. Each triangle has a right angle symbol and one tick mark on a side adjacent to the right angle. The handwritten answer says "ASA".
- Next, find information: I need to verify if the markings correspond to the Angle-Side-Angle (ASA) postulate.
- Then, review the findings: ASA requires two angles and the included side to be equal. Here, we have one right angle in each triangle, but we don't have information about the second angle or the included side between the two angles. The tick marks indicate one side is equal, but without knowing the second angle, we cannot apply ASA. This seems incorrect.
- First, look closely: Two triangles are shown with three sides marked with tick marks: one, two, and three tick marks respectively. The handwritten answer is "SSS".
- Next, find information: SSS (Side-Side-Side) means all three sides of one triangle are equal to the corresponding sides of another triangle.
- Then, review the findings: Since all three sides are marked with matching tick marks (one tick, two ticks, three ticks), this satisfies the SSS postulate. The handwritten answer "SSS" is correct.
- First, look closely: Two triangles are shown with one side marked with a single tick and one angle marked with an arc. The handwritten answer is "ASA".
- Next, find information: I need to verify if this matches the ASA postulate.
- Then, review the findings: ASA requires two angles and the included side. Here, we have only one angle and one side marked. Without a second angle, we cannot apply ASA. This seems incorrect.
- First, look closely: Two triangles are shown with different markings. One has two tick marks on one side and an angle marked, while the other has one tick mark on a side and an angle marked. The handwritten answer is "not congruent".
- Next, find information: I need to determine if any congruence postulate applies.
- Then, review the findings: The markings do not correspond between the two triangles. The number of tick marks on the sides is different, and the angles are not clearly corresponding. Therefore, the triangles are not congruent. The handwritten answer "not congruent" is correct.
- First, look closely: Two right triangles are shown with a common side. Both have a right angle symbol and one tick mark on a leg. The handwritten answer is "ASA".
- Next, find information: I need to verify if this matches the ASA postulate.
- Then, review the findings: Both triangles have a right angle, and they share a side (which could be considered the included side). However, we need a second angle to apply ASA. The diagram does not provide enough information about the second angle. This seems incorrect.
- First, look closely: Two triangles are shown with two sides marked with tick marks and one angle marked. The handwritten answer is "not congruent".
- Next, find information: I need to determine if any congruence postulate applies.
- Then, review the findings: The markings do not correspond between the two triangles. The number of tick marks on the sides is different, and the angles are not clearly corresponding. Therefore, the triangles are not congruent. The handwritten answer "not congruent" is correct.
- First, look closely: Two triangles are shown with three sides marked with tick marks: one, two, and three tick marks respectively. The handwritten answer is "SSS".
- Next, find information: SSS (Side-Side-Side) means all three sides of one triangle are equal to the corresponding sides of another triangle.
- Then, review the findings: Since all three sides are marked with matching tick marks (one tick, two ticks, three ticks), this satisfies the SSS postulate. The handwritten answer "SSS" is correct.
- First, look closely: Two triangles are shown with two sides marked with tick marks and one angle marked. The handwritten answer is "SAS".
- Next, find information: I need to verify if this matches the Side-Angle-Side (SAS) postulate.
- Then, review the findings: SAS requires two sides and the included angle to be equal. Here, we have two sides marked with tick marks and an angle marked, which appears to be the included angle between the two sides. This satisfies the SAS postulate. The handwritten answer "SAS" is correct.
- First, look closely: Two triangles are shown with three sides marked with tick marks: one, two, and three tick marks respectively. The handwritten answer is "SSS".
- Next, find information: SSS (Side-Side-Side) means all three sides of one triangle are equal to the corresponding sides of another triangle.
- Then, review the findings: Since all three sides are marked with matching tick marks (one tick, two ticks, three ticks), this satisfies the SSS postulate. The handwritten answer "SSS" is correct.
- First, look closely: These problems ask for additional information required to prove congruence using ASA and SAS, respectively. The diagrams show quadrilaterals with some markings.
- Next, find information: I need to recall what additional information is needed for ASA and SAS.
- Then, review the findings:
- For ASA, we need two angles and the included side. If we already have one angle and the included side, we need the second angle.
- For SAS, we need two sides and the included angle. If we already have two sides, we need the included angle.
Based on my analysis, I will now provide a synthesized answer.
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Synthesized Answer:
Here is the evaluation of each problem:
1. Not Congruent - Correct. Only one side is marked as equal, insufficient for congruence.
2. Incorrect - The markings do not satisfy ASA. We need two angles and the included side.
3. SSS - Correct. All three sides are marked as equal.
4. Incorrect - The markings do not satisfy ASA. We need two angles and the included side.
5. Not Congruent - Correct. The markings do not correspond between the triangles.
6. Incorrect - The markings do not satisfy ASA. We need two angles and the included side.
7. Not Congruent - Correct. The markings do not correspond between the triangles.
8. SSS - Correct. All three sides are marked as equal.
9. SAS - Correct. Two sides and the included angle are marked as equal.
10. SSS - Correct. All three sides are marked as equal.
For problems 11 and 12:
- Problem 11 (ASA): Additional information required is the second angle.
- Problem 12 (SAS): Additional information required is the included angle.
The handwritten answers are mostly correct, except for problems 2, 4, and 6, where ASA was incorrectly applied.
Let me start by looking closely at each numbered problem.
Problem 1
- First, look closely: The first image shows two triangles sharing a side. One triangle has one tick mark on its base and one tick mark on its left side. The other triangle has one tick mark on its right side. There is a handwritten note "not congruent".
- Next, find information: I need to recall the triangle congruence postulates. For two triangles to be congruent, we need three corresponding parts to be equal (with specific arrangements: SSS, SAS, ASA, AAS, or HL for right triangles).
- Then, review the findings: In this case, we have only one pair of sides marked as equal (the shared side), and no other corresponding sides or angles are marked. Therefore, we cannot conclude that the triangles are congruent. The handwritten answer "not congruent" appears to be correct.
Problem 2
- First, look closely: This image shows two triangles with a common vertex. Each triangle has a right angle symbol and one tick mark on a side adjacent to the right angle. The handwritten answer says "ASA".
- Next, find information: I need to verify if the markings correspond to the Angle-Side-Angle (ASA) postulate.
- Then, review the findings: ASA requires two angles and the included side to be equal. Here, we have one right angle in each triangle, but we don't have information about the second angle or the included side between the two angles. The tick marks indicate one side is equal, but without knowing the second angle, we cannot apply ASA. This seems incorrect.
Problem 3
- First, look closely: Two triangles are shown with three sides marked with tick marks: one, two, and three tick marks respectively. The handwritten answer is "SSS".
- Next, find information: SSS (Side-Side-Side) means all three sides of one triangle are equal to the corresponding sides of another triangle.
- Then, review the findings: Since all three sides are marked with matching tick marks (one tick, two ticks, three ticks), this satisfies the SSS postulate. The handwritten answer "SSS" is correct.
Problem 4
- First, look closely: Two triangles are shown with one side marked with a single tick and one angle marked with an arc. The handwritten answer is "ASA".
- Next, find information: I need to verify if this matches the ASA postulate.
- Then, review the findings: ASA requires two angles and the included side. Here, we have only one angle and one side marked. Without a second angle, we cannot apply ASA. This seems incorrect.
Problem 5
- First, look closely: Two triangles are shown with different markings. One has two tick marks on one side and an angle marked, while the other has one tick mark on a side and an angle marked. The handwritten answer is "not congruent".
- Next, find information: I need to determine if any congruence postulate applies.
- Then, review the findings: The markings do not correspond between the two triangles. The number of tick marks on the sides is different, and the angles are not clearly corresponding. Therefore, the triangles are not congruent. The handwritten answer "not congruent" is correct.
Problem 6
- First, look closely: Two right triangles are shown with a common side. Both have a right angle symbol and one tick mark on a leg. The handwritten answer is "ASA".
- Next, find information: I need to verify if this matches the ASA postulate.
- Then, review the findings: Both triangles have a right angle, and they share a side (which could be considered the included side). However, we need a second angle to apply ASA. The diagram does not provide enough information about the second angle. This seems incorrect.
Problem 7
- First, look closely: Two triangles are shown with two sides marked with tick marks and one angle marked. The handwritten answer is "not congruent".
- Next, find information: I need to determine if any congruence postulate applies.
- Then, review the findings: The markings do not correspond between the two triangles. The number of tick marks on the sides is different, and the angles are not clearly corresponding. Therefore, the triangles are not congruent. The handwritten answer "not congruent" is correct.
Problem 8
- First, look closely: Two triangles are shown with three sides marked with tick marks: one, two, and three tick marks respectively. The handwritten answer is "SSS".
- Next, find information: SSS (Side-Side-Side) means all three sides of one triangle are equal to the corresponding sides of another triangle.
- Then, review the findings: Since all three sides are marked with matching tick marks (one tick, two ticks, three ticks), this satisfies the SSS postulate. The handwritten answer "SSS" is correct.
Problem 9
- First, look closely: Two triangles are shown with two sides marked with tick marks and one angle marked. The handwritten answer is "SAS".
- Next, find information: I need to verify if this matches the Side-Angle-Side (SAS) postulate.
- Then, review the findings: SAS requires two sides and the included angle to be equal. Here, we have two sides marked with tick marks and an angle marked, which appears to be the included angle between the two sides. This satisfies the SAS postulate. The handwritten answer "SAS" is correct.
Problem 10
- First, look closely: Two triangles are shown with three sides marked with tick marks: one, two, and three tick marks respectively. The handwritten answer is "SSS".
- Next, find information: SSS (Side-Side-Side) means all three sides of one triangle are equal to the corresponding sides of another triangle.
- Then, review the findings: Since all three sides are marked with matching tick marks (one tick, two ticks, three ticks), this satisfies the SSS postulate. The handwritten answer "SSS" is correct.
Problems 11 and 12
- First, look closely: These problems ask for additional information required to prove congruence using ASA and SAS, respectively. The diagrams show quadrilaterals with some markings.
- Next, find information: I need to recall what additional information is needed for ASA and SAS.
- Then, review the findings:
- For ASA, we need two angles and the included side. If we already have one angle and the included side, we need the second angle.
- For SAS, we need two sides and the included angle. If we already have two sides, we need the included angle.
Based on my analysis, I will now provide a synthesized answer.
---
Synthesized Answer:
Here is the evaluation of each problem:
1. Not Congruent - Correct. Only one side is marked as equal, insufficient for congruence.
2. Incorrect - The markings do not satisfy ASA. We need two angles and the included side.
3. SSS - Correct. All three sides are marked as equal.
4. Incorrect - The markings do not satisfy ASA. We need two angles and the included side.
5. Not Congruent - Correct. The markings do not correspond between the triangles.
6. Incorrect - The markings do not satisfy ASA. We need two angles and the included side.
7. Not Congruent - Correct. The markings do not correspond between the triangles.
8. SSS - Correct. All three sides are marked as equal.
9. SAS - Correct. Two sides and the included angle are marked as equal.
10. SSS - Correct. All three sides are marked as equal.
For problems 11 and 12:
- Problem 11 (ASA): Additional information required is the second angle.
- Problem 12 (SAS): Additional information required is the included angle.
The handwritten answers are mostly correct, except for problems 2, 4, and 6, where ASA was incorrectly applied.
Parent Tip: Review the logic above to help your child master the concept of sas sss asa aas worksheet.
