✓ Board-verified↻ asked 3×
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 $\displaystyle \mathrm{AB}=\mathrm{AC}$. 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
- Which of the following statements is incorrect?2025 · asked 3×
- E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that Δ ABE Δ…2024 · asked 3×
- If PQR ABC; PQ=6 cm, AB=8 cm and the perimeter of ABC is 36 cm, then the perimeter of PQR is2023 · asked 3×
- 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…2025 · asked 3×
- If Δ ABC Δ PQR with ∠ A=32^° and ∠ R=65^°, then the measure of ∠ B is:2023 · asked 3×
- In triangles ABC and DEF, ∠ B=∠ E, ∠ F=∠ C and AB=3 DE. Then, the two triangles are:2025 · asked 3×
- In the given figure, DE BC. If AD=3 cm, AB=7 cm and EC=3 cm, then the length of AE is2023 · asked 3×
- In the given figure, in Δ ABC, AD ⊥ BC and ∠ BAC=90^°. If BC=16 cm and DC=4 cm, then the value of x is:2025 · asked 3×
CBSE Class 10 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.