Q: State and prove the Pythagoras Theorem (Theorem 6.8 of NCERT Class 10 Mathematics).

Statement of Pythagoras Theorem\nIn a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Given Data\nLet $\triangle ABC$ be a right-angled triangle, right-angled at $B$ (i.e., $\angle B = 90^\circ$). To Prove $$AC^2 = AB^2 + BC^2$$ Construction\nD

Q: State and prove the Basic Proportionality Theorem (Thales's Theorem). Also, in triangle ABC, DE is parallel to BC intersecting AB at D and AC at E. If AD = 1.5 cm, DB = 3 cm, and AE = 1 cm, find the l

Statement of Thales's Theorem:\nIf a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Proof: Given: In $\triangle ABC$, $DE \parallel BC$, intersecting $AB$ at $D$ and $AC$ at $E$. To Prove: $\fra

Question 1

Diagonals $AC$ and $BD$ of a trapezium $ABCD$ with $AB \parallel DC$ intersect each other at the point $O$. Using a similarity criterion for triangles, show that $\frac{AO}{OC} = \frac{BO}{OD}$.

Accepted Answer

Solution: Given: A trapezium $ABCD$ in which $AB \parallel DC$ and diagonals $AC$ and $BD$ intersect at point $O$. To Show: $\frac{AO}{OC} = \frac{BO}{OD}$ Proof Steps: Consider triangle $AOB$ and triangle $COD$. Since $AB \parallel DC$ and $BD$ is a transversal line, the alternate interior angles a

Question 2

State and prove the Pythagoras Theorem (Theorem 6.8 of NCERT Class 10 Mathematics).

Accepted Answer

Statement of Pythagoras Theorem
In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Given Data
Let $	riangle ABC$ be a right-angled triangle, right-angled at $B$ (i.e., $\angle B = 90^\circ$). To Prove $$AC^2 = AB^2 + BC^2$$ Construction
D

Question 3

State and prove the Basic Proportionality Theorem (Thales's Theorem). Also, in triangle ABC, DE is parallel to BC intersecting AB at D and AC at E. If AD = 1.5 cm, DB = 3 cm, and AE = 1 cm, find the l

Accepted Answer

Statement of Thales's Theorem:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Proof: Given: In $	riangle ABC$, $DE \parallel BC$, intersecting $AB$ at $D$ and $AC$ at $E$. To Prove: $\fra

Triangles