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Stay Home , Stay Safe and keep learning!!! AA similarity : If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
Paragraph proof :
Let ΔABC and ΔDEF be two triangles such that ∠A = ∠D and ∠B = ∠E.
∠A + ∠B + ∠C = 180 0 (Sum of all angles in a Δ is 180)
∠D + ∠E + ∠F = 180 0 (Sum of all angles in a Δ is 180)
⇒ ∠A + ∠B + ∠C = ∠D + ∠E + ∠F
⇒ ∠D + ∠E + ∠C = ∠D + ∠E + ∠F (since ∠A = ∠D and ∠B = ∠E)
⇒ ∠C = ∠F
Thus the two triangles are equiangular and hence they are similar by AA.
1) D is a point on the side of BC of ΔABC such that ∠ADC = ∠BAC.
Prove that CA 2 = BA x CD
Given : ∠ADC = ∠BAC
Prove that : CA 2 = BA x CD
| 1) ∠ADC = ∠BAC
|| 1) Given
| 2) ∠C = ∠C
|| 2) Reflexive (common)
| 3) ΔABC ~ ΔDAC
|| 3) AA criteria (postulate)
| 4) AB/DA = CB/CA = CA/CD
|| 4) If two triangles are similar then their sides are in proportion.
| 5) CB/CA = CA /CD
|| 5) Last two ratios
6) CA2 = CB x CD
|| 6) Cross multiplication .
2) In the given figure, DE||BC such that AE=(1/4)AC. If AB= 6 cm, then find the value of AD.
Solution : As DE || BC,
⇒ AE/AC = 1/4
ΔABC ~ ΔADE -----> A-A-similarity
∴ AD/AB = AE/AC
AD/6 = 1/4
AD = (6 x1)/4
AD = 1.5cm.
Criteria for Similarity
• A-A-A- Similarity
• AA Similarity
• SSS Similarity
• SAS Similarity
• Practice on Similarity
To Criteria for Similarity of Triangles
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