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


Problem on Two Isosceles Triangles on the Same Base

Here we will prove that ∆PQR and ∆SQR are two isosceles triangles drawn on the same base QR and on the same side of it. If P and S be joined, prove that each of the angles ∠QPR and ∠QSR will be divided by the line PS into two equal parts.

Two Isosceles Triangles on the Same Base

Solution:

Given: PQ = PR and SQ = SR to prove ∠QPS = ∠ RPS and ∠QST = ∠RST

Proof:

               Statement

1. In ∆PQR, ∠PQR = ∠PRQ = x° (Suppose)

2. In ∆SQR, ∠SQR = ∠SRQ = y° (Suppose).

3. ∠PQR - ∠SQR = ∠PRQ - ∠SRQ = x° - y°

4. Therefore, ∠PQS = ∠PRS = x° - y°

5. In ∆PQS and ∆PRS,

(i) PQ = PR

(ii) SQ = SR

(iii) ∠PQS = ∠PRS


6. ∆PQS ≅ ∆PRS

7. ∠QPS = ∠RPS = z° (Suppose).

8. ∠QST = ∠PQS + ∠QPS = x° - y° + z°

9. Similarly, ∠RST = ∠PRS + ∠RPS = x° - y° + z°

10. ∠QST = ∠RST (Proved)

               Reason

1. PQ = PR


2. SQ = SR

3. Subtracting statement 2 from statement 1.

4. From statement 3.


5.

(i) Given.

(ii) Given.

(iii) From statement 4.


6. By SAS criterion

7. CPCTC

8. The exterior angle of a triangle is equal to the sum of the interior opposite angles.

9. As above.

10. From statements 8 and 9.




9th Grade Math

From Problem on Two Isosceles Triangles on the Same Base 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

RSS

  1. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  2. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  3. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More