Question:
Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
Sides $AB$ and $BC$ and median $AD$ of a $△ABC$ are respectively proportional to sides $PQ$ and $PR$ and median $PM$ of $△PQR$. Show that $△ABC ∼ △PQR$.
Updated On: Dec 14, 2024
Hide Solution
Verified By Collegedunia
Solution and Explanation
- Let \( \triangle ABC \) and \( \triangle PQR \) be two triangles such that the sides \( AB \parallel PQ \), \( BC \parallel PR \), and \( AD \parallel PM \).
- Since the corresponding sides are proportional, we can use the criteria for similarity of triangles:
\[ \frac{AB}{PQ} = \frac{BC}{PR} = \frac{AD}{PM} \]
- Therefore, by the Side-Side-Side (SSS) similarity criterion, \( \triangle ABC \sim \triangle PQR \).
Was this answer helpful?
0
0
Top Questions on Triangles
- In \( \triangle ABC \), if \( r_1 = 4 \), \( r_2 = 8 \), \( r_3 = 24 \), then find \( a \)=
- In \( \triangle ABC \), if \( a = 13 \), \( b = 14 \), and \( \cos \frac{C}{2} = \frac{3}{\sqrt{13}} \), then \( 2r_1 = \):
- If 7 and 8 are the lengths of two sides of a triangle and \( a \) is the length of its smallest side. The angles of the triangle are in AP and \( a \) has two values \( a_1 \) and \( a_2 \) satisfying this condition. If \( a_1 < a_2 \), then \( 2a_1 + 3a_2 = \):
- In \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
- If the orthocentre of the triangle formed by the lines 2x + 3y – 1 = 0, x + 2y – 1 = 0 and ax + by – 1 = 0, is the centroid of another triangle, whose circumecentre and orthocentre respectively are (3, 4) and (–6, –8), then the value of |a– b| is_____.
View More Questions
Questions Asked in CBSE X exam
- The sum of two numbers is 18, and the sum of their reciprocals is $\frac{1}{4}$. Find the numbers.
- CBSE Class X - 2024
- Linear Equations
- The vertices of a quadrilateral ABCD are A(6, – 2), B(9, 2), C(5, – 1) and D(2, – 5). Prove that ABCD is a rhombus, and not a square.
- CBSE Class X - 2024
- Coordinate Geometry
- $ABCD$ is a trapezium with $AB \parallel DC$. $AC$ and $BD$ intersect at $E$. If $\triangle AED \sim \triangle BEC$, then prove that $AD = BC$.
- CBSE Class X - 2024
- Similarity of Triangles
- The sum of the first three terms of an AP is 30 and the sum of the last three terms is 36. If the first term is 9, then the number of terms is :
- CBSE Class X - 2024
- Arithmetic Progression
- Write down the difference between sight alignment and sight picture.
- CBSE Class X - 2024
- Weapon Training
View More Questions