Subscribe to our YouTube channel for the latest videos, updates, and tips.


AA Criterion of Similarly on Quadrilateral

Here we will prove the theorems related to AA Criterion of Similarity.

1. In the quadrilateral ABCD, AB CD. Prove that OA × OD = OB × OC.

AA Criterion of Similarly on Quadrilateral

Solution:

Proof:

            Statement

            Reason

1. In ∆ OAB and ∆OCD,

(i) ∠AOB = ∠COD

(ii) ∠OBA = ∠ODC.

1.

(i) Vertically opposite angles.

(ii) Alternate angles.

2. ∆ OAB ∼ ∆OCD.

2. By AA criterion of similarly.

3. Therefore, \(\frac{OA}{OC}\) = \(\frac{OB}{OD}\)

⟹ OA × OD = OB × OC. (Proved)

3. Corrosponding sides of similar triangles are proportional.


2. In the quadrilateral PQRS, PQ ∥ RS. T is any point on PS. QT is joined and produced to meet RS produced at U. Prove that \(\frac{PQ}{SU}\) = \(\frac{PT}{TS}\).

Similarly on Quadrilateral

Solution:

Proof:

            Statement

            Reason

1. In ∆PQT and ∆SUT,

(i) ∠PTQ = ∠STU

(ii) ∠QPT = ∠TSU

1.

(i) Vertically opposite angles are equal

(ii) Alternate angles are equal

2. ∆PQT ∼ ∆SUT

2. By AA criterion of similarity

3. \(\frac{PQ}{SU}\) = \(\frac{PT}{TS}\). (Proved)

3. Corresponding sides of similar triangles are proportional.





9th Grade Math

From AA Criterion of Similarly on Quadrilateral to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Conversion of Improper Fractions into Mixed Fractions |Solved Examples

    May 12, 25 04:52 AM

    Conversion of Improper Fractions into Mixed Fractions
    In conversion of improper fractions into mixed fractions, we follow the following steps: Step I: Obtain the improper fraction. Step II: Divide the numerator by the denominator and obtain the quotient…

    Read More

  2. Multiplication Table of 6 | Read and Write the Table of 6 | Six Table

    May 12, 25 02:23 AM

    Multiplication Table of Six
    Repeated addition by 6’s means the multiplication table of 6. (i) When 6 bunches each having six bananas each. By repeated addition we can show 6 + 6 + 6 + 6 + 6 + 6 = 36 Then, six 6 times or 6 sixes

    Read More

  3. Word Problems on Decimals | Decimal Word Problems | Decimal Home Work

    May 11, 25 01:22 PM

    Word problems on decimals are solved here step by step. The product of two numbers is 42.63. If one number is 2.1, find the other. Solution: Product of two numbers = 42.63 One number = 2.1

    Read More

  4. Worksheet on Dividing Decimals | Huge Number of Decimal Division Prob

    May 11, 25 11:52 AM

    Worksheet on Dividing Decimals
    Practice the math questions given in the worksheet on dividing decimals. Divide the decimals to find the quotient, same like dividing whole numbers. This worksheet would be really good for the student…

    Read More

  5. Worksheet on Multiplying Decimals | Product of the Two Decimal Numbers

    May 11, 25 11:18 AM

    Practice the math questions given in the worksheet on multiplying decimals. Multiply the decimals to find the product of the two decimal numbers, same like multiplying whole numbers.

    Read More