Looking at problem 9, I see a quadrilateral JKLM with diagonal KM drawn. The markings indicate:
- Side JK is congruent to side LM (indicated by the single tick marks).
- Side JM is congruent to side KL (indicated by the double tick marks).
- Side KM is common to both triangles JKM and LMK.
This means we have all three sides of triangle JKM congruent to all three sides of triangle LMK.
The postulate that states if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent is the Side-Side-Side (SSS) Postulate.
Therefore, for problem 9, the answer is SSS (Side-Side-Side).
Now, let me move on to problem 10.
Looking at problem 10, I see a quadrilateral NOPQ with diagonal NP drawn. The markings indicate:
- Angle ONP is congruent to angle QNP (indicated by the single arc marks).
- Angle OPN is congruent to angle QPN (indicated by the double arc marks).
- Side NP is common to both triangles NOP and QNP.
This means we have two angles and the included side of triangle NOP congruent to two angles and the included side of triangle QNP.
The postulate that states 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 is the Angle-Side-Angle (ASA) Postulate.
Therefore, for problem 10, the answer is ASA (Angle-Side-Angle).
Now, let me move on to problem 11.
Looking at problem 11, I see a quadrilateral JKLM with diagonal KM drawn. The markings indicate:
- Side JK is congruent to side LM (indicated by the single tick marks).
- Angle JKM is congruent to angle LMK (indicated by the single arc marks).
- Side KM is common to both triangles JKM and LMK.
This means we have two sides and the included angle of triangle JKM congruent to two sides and the included angle of triangle LMK.
The postulate that states 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 is the Side-Angle-Side (SAS) Postulate.
Therefore, for problem 11, the answer is SAS (Side-Angle-Side).
Finally, let me move on to problem 12.
Looking at problem 12, I see a square RSTU with diagonal SU drawn. The markings indicate:
- Side RS is congruent to side UT (indicated by the single tick marks).
- Side ST is congruent to side RU (indicated by the double tick marks).
- Side SU is common to both triangles RSU and TUS.
This means we have all three sides of triangle RSU congruent to all three sides of triangle TUS.
The postulate that states if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent is the Side-Side-Side (SSS) Postulate.
Therefore, for problem 12, the answer is SSS (Side-Side-Side).
Here are the answers for all 12 problems:
1. SAS (Side-Angle-Side)
2. SSS (Side-Side-Side)
3. ASA (Angle-Side-Angle)
4. AAS (Angle-Angle-Side)
5. ASA (Angle-Side-Angle)
6. SAS (Side-Angle-Side)
7. ASA (Angle-Side-Angle)
8. AAS (Angle-Angle-Side)
9. SSS (Side-Side-Side)
10. ASA (Angle-Side-Angle)
11. SAS (Side-Angle-Side)
12. SSS (Side-Side-Side)
Parent Tip: Review the logic above to help your child master the concept of congruence of triangles worksheet.
![FREE Printable Triangle Congruence Worksheets [PDFs] Brighterly](/images2/congruence-of-triangles-worksheet/congruence-of-triangles-worksheet-26.jpg)
