✓ Board-verified
Mathematics · 2023 · 3 marks
CBSE 2023 · Region 6 · Set 1 · Q28
In the given figure, E is a point on the side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, then prove that ABD ∼…
In the given figure, E is a point on the side CB produced of an isosceles triangle ABC with $\displaystyle \mathrm{AB}=\mathrm{AC}$. If $\displaystyle \mathrm{AD} \perp \mathrm{BC}$ and $\displaystyle \mathrm{EF} \perp \mathrm{AC}$, then prove that $\displaystyle \triangle \mathrm{ABD} \sim \triangle \mathrm{ECF}$.
Marking-scheme solution
ABC is an isosceles triangle
\[\therefore A B=A C \Rightarrow \angle B=\angle C
\]
In \(\displaystyle \Delta \mathrm{ABD}\) and \(\displaystyle \Delta \mathrm{ECF}\),
\[\angle \mathrm{ADB}=\angle \mathrm{EFC}
\]
\[\angle \mathrm{ABD}=\angle \mathrm{ECF}
\]
\[\therefore \triangle \mathrm{ABD} \sim \triangle \mathrm{ECF}
\]
More from Triangles
- Sides AB and AC and median AM of a ABC are proportional to sides DE and DF and Median DN of another DEF. Show that ABC ∼ DEF. ABCD is a…2023
- In the given figure, DE ∥ BC. If AD=2 units, DB=AE=3 units and EC=x units, then the value of x is:2023
- Which of the following statements is incorrect?2025
- E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE ∼ Δ CFB. OR Sides AB, BC and the median AD of…2024
- If PQR ∼ ABC; PQ=6 cm, AB=8 cm and the perimeter of ABC is 36 cm, then the perimeter of PQR is2023
- In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that:2024
- E and F are points on the sides AB and AC respectively of a ABC such that AE/EB=AF/FC=1/2. Which of the following relation is true?2025
- If Δ ABC ∼ Δ PQR with ∠ A=32^° and ∠ R=65^°, then the measure of ∠ B is:2023
CBSE Class 10 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.