4-SSS, SAS, ASA, and AAS Congruence.pdf - Kuta Software - Free Printable
Educational worksheet: 4-SSS, SAS, ASA, and AAS Congruence.pdf - Kuta Software. Download and print for classroom or home learning activities.
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Step-by-step solution for: 4-SSS, SAS, ASA, and AAS Congruence.pdf - Kuta Software
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Show Answer Key & Explanations
Step-by-step solution for: 4-SSS, SAS, ASA, and AAS Congruence.pdf - Kuta Software
I will solve this geometry worksheet by examining each pair of triangles and determining if they are congruent based on the SSS, SAS, ASA, or AAS congruence postulates. I'll go through each problem one by one.
Let me start with problem 1.
Problem 1:
- First, look closely: The image shows two triangles that share a side. Both triangles have markings indicating that two sides and the included angle are equal. Specifically, there are tick marks on two sides of each triangle and an arc marking the angle between them.
- Next, find information: I need to recall the triangle congruence postulates:
- SSS (Side-Side-Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
- SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
- ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
- AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.
- Then, review the findings: Based on the markings, this is a clear case of SAS congruence since we have two sides and the included angle marked as equal.
Problem 2:
- First, look closely: This shows two triangles sharing a side. There are tick marks on two sides of each triangle and arcs marking the angles at the endpoints of the shared side.
- Next, find information: I need to determine which congruence postulate applies here.
- Then, review the findings: The markings indicate that we have two angles and the included side equal (the shared side), which corresponds to ASA congruence.
Problem 3:
- First, look closely: Two triangles are shown with markings on all three sides.
- Next, find information: I need to check if all three sides are marked as equal.
- Then, review the findings: All three sides of each triangle have matching tick marks, indicating SSS congruence.
Problem 4:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle relative to the marked sides.
- Then, review the findings: The marked angle is not between the two marked sides, so this is AAS congruence.
Problem 5:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is between the two marked sides, so this is SAS congruence.
Problem 6:
- First, look closely: Two right triangles are shown with markings on two sides and the right angle.
- Next, find information: I need to determine which sides are marked and their relationship to the right angle.
- Then, review the findings: One leg and the hypotenuse are marked as equal in both triangles, which corresponds to HL (Hypotenuse-Leg) congruence for right triangles. However, since HL is not listed in the worksheet's title, I should note that this is a special case of SSA which only works for right triangles.
Problem 7:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is not between the two marked sides, so this is AAS congruence.
Problem 8:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is between the two marked sides, so this is SAS congruence.
Problem 9:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is not between the two marked sides, so this is AAS congruence.
Problem 10:
- First, look closely: Two triangles are shown with markings on all three sides.
- Next, find information: I need to check if all three sides are marked as equal.
- Then, review the findings: All three sides of each triangle have matching tick marks, indicating SSS congruence.
Now I'll provide the final answers for each problem:
1. Congruent by SAS
2. Congruent by ASA
3. Congruent by SSS
4. Congruent by AAS
5. Congruent by SAS
6. Congruent by HL (Hypotenuse-Leg, a special case for right triangles)
7. Congruent by AAS
8. Congruent by SAS
9. Congruent by AAS
10. Congruent by SSS
Let me start with problem 1.
Problem 1:
- First, look closely: The image shows two triangles that share a side. Both triangles have markings indicating that two sides and the included angle are equal. Specifically, there are tick marks on two sides of each triangle and an arc marking the angle between them.
- Next, find information: I need to recall the triangle congruence postulates:
- SSS (Side-Side-Side): If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.
- SAS (Side-Angle-Side): If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
- ASA (Angle-Side-Angle): If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent.
- AAS (Angle-Angle-Side): If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, the triangles are congruent.
- Then, review the findings: Based on the markings, this is a clear case of SAS congruence since we have two sides and the included angle marked as equal.
Problem 2:
- First, look closely: This shows two triangles sharing a side. There are tick marks on two sides of each triangle and arcs marking the angles at the endpoints of the shared side.
- Next, find information: I need to determine which congruence postulate applies here.
- Then, review the findings: The markings indicate that we have two angles and the included side equal (the shared side), which corresponds to ASA congruence.
Problem 3:
- First, look closely: Two triangles are shown with markings on all three sides.
- Next, find information: I need to check if all three sides are marked as equal.
- Then, review the findings: All three sides of each triangle have matching tick marks, indicating SSS congruence.
Problem 4:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle relative to the marked sides.
- Then, review the findings: The marked angle is not between the two marked sides, so this is AAS congruence.
Problem 5:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is between the two marked sides, so this is SAS congruence.
Problem 6:
- First, look closely: Two right triangles are shown with markings on two sides and the right angle.
- Next, find information: I need to determine which sides are marked and their relationship to the right angle.
- Then, review the findings: One leg and the hypotenuse are marked as equal in both triangles, which corresponds to HL (Hypotenuse-Leg) congruence for right triangles. However, since HL is not listed in the worksheet's title, I should note that this is a special case of SSA which only works for right triangles.
Problem 7:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is not between the two marked sides, so this is AAS congruence.
Problem 8:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is between the two marked sides, so this is SAS congruence.
Problem 9:
- First, look closely: Two triangles are shown with markings on two sides and one angle.
- Next, find information: I need to determine the position of the marked angle.
- Then, review the findings: The marked angle is not between the two marked sides, so this is AAS congruence.
Problem 10:
- First, look closely: Two triangles are shown with markings on all three sides.
- Next, find information: I need to check if all three sides are marked as equal.
- Then, review the findings: All three sides of each triangle have matching tick marks, indicating SSS congruence.
Now I'll provide the final answers for each problem:
1. Congruent by SAS
2. Congruent by ASA
3. Congruent by SSS
4. Congruent by AAS
5. Congruent by SAS
6. Congruent by HL (Hypotenuse-Leg, a special case for right triangles)
7. Congruent by AAS
8. Congruent by SAS
9. Congruent by AAS
10. Congruent by SSS
Parent Tip: Review the logic above to help your child master the concept of triangle congruence by sss and sas worksheet answers.
