AA Similarity

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

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 = 1800 (Sum of all angles in a Δ is 180)

∠D + ∠E + ∠F = 1800(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 CA2 = BA x CD
Given : ∠ADC = ∠BAC
Prove that : CA2 = 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/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

Home Page

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.