Which pair of triangles can be proven congruent by SAS?

Which pair of triangles can be proven congruent by SAS?

Answer: Option B

What is SAS Congruence?

The Side-Angle-Side (SAS) congruence rule states that:

If two sides and the included angle between them in one triangle are equal to the corresponding two sides and included angle in another triangle, then the triangles are congruent.

Explanation of Option B

In the diagram, triangle ADB and triangle ADC are formed by drawing line segment AD inside triangle ABC.

We can observe the following:

1. AD = AD → common side (reflexive property)

2. BD = DC → indicated by matching tick marks

3. ∠ADB = ∠ADC → both are right angles

The angle given (∠ADB and ∠ADC) lies between the two equal sides (AD & BD / AD & DC), making it the included angle.

Since:

Two corresponding sides are equal and the included angle between them is equal, therefore,

ADB ≅ ADC by SAS congruence rule

How to identify SAS in any diagram

To check if triangles are congruent using SAS:

1. Look for two pairs of equal sides

2. Check if the angle between those sides is equal

3. Ensure the angle is included (not outside the sides)

Final Conclusion

Option B is correct because triangles ADB and ADC satisfy the Side-Angle-Side (SAS) congruence condition, making them congruent.

Under deadline pressure? Sign up on Locus Assignments login for academic support– order your assignment today!