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in a quadrilateral ABCD AB =AD and AC bisects angle A show that triangle ABC congruent triangle ABD
Most Upvoted Answer
in a quadrilateral ABCD AB =AD and AC bisects angle A show that triang...
Given= AB=AD
ABCD is a quadrilateral
To Prove=traingle ABC congurent to ABD
proof=In traingle ABD and ABC
AB=AB (common side )
Angle A=Angle A (common angle )
AB =AD (given)
Traingle ABC congurent to ABD (by SAS congurrnce rule )
hence proved
ABCD is a quadrilateral
To Prove=traingle ABC congurent to ABD
proof=In traingle ABD and ABC
AB=AB (common side )
Angle A=Angle A (common angle )
AB =AD (given)
Traingle ABC congurent to ABD (by SAS congurrnce rule )
hence proved
Community Answer
in a quadrilateral ABCD AB =AD and AC bisects angle A show that triang...
Given:
- Quadrilateral ABCD
- AB = AD
- AC bisects angle A
To prove:
Triangle ABC ≅ Triangle ABD
Proof:
Step 1: Draw a diagram
- Draw the quadrilateral ABCD
- Mark the points A, B, C, and D
- Draw the line AC bisecting angle A
Step 2: Given conditions
- AB = AD (Given)
- AC bisects angle A (Given)
Step 3: Statement and reason
- ∠BAC = ∠DAC (Angle bisector divides the angle into two equal parts)
- AB = AD (Given)
- AC = AC (Common side)
Step 4: Apply SAS congruence criterion
- Triangle ABC ≅ Triangle ABD (By SAS congruence criterion)
- ∠BAC = ∠DAC (From step 3)
- AB = AD (From step 3)
- AC = AC (From step 3)
Step 5: Conclusion
- Triangle ABC ≅ Triangle ABD by SAS congruence criterion (From step 4)
Summary:
In the given quadrilateral ABCD, where AB = AD and AC bisects angle A, we have proved that triangle ABC is congruent to triangle ABD using the SAS congruence criterion.
- Quadrilateral ABCD
- AB = AD
- AC bisects angle A
To prove:
Triangle ABC ≅ Triangle ABD
Proof:
Step 1: Draw a diagram
- Draw the quadrilateral ABCD
- Mark the points A, B, C, and D
- Draw the line AC bisecting angle A
Step 2: Given conditions
- AB = AD (Given)
- AC bisects angle A (Given)
Step 3: Statement and reason
- ∠BAC = ∠DAC (Angle bisector divides the angle into two equal parts)
- AB = AD (Given)
- AC = AC (Common side)
Step 4: Apply SAS congruence criterion
- Triangle ABC ≅ Triangle ABD (By SAS congruence criterion)
- ∠BAC = ∠DAC (From step 3)
- AB = AD (From step 3)
- AC = AC (From step 3)
Step 5: Conclusion
- Triangle ABC ≅ Triangle ABD by SAS congruence criterion (From step 4)
Summary:
In the given quadrilateral ABCD, where AB = AD and AC bisects angle A, we have proved that triangle ABC is congruent to triangle ABD using the SAS congruence criterion.
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in a quadrilateral ABCD AB =AD and AC bisects angle A show that triangle ABC congruent triangle ABD Related: Polynomials in One Variable and Degree of a Polynomial - Polynomials, Class 9, Mathematics
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