E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.
E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABE ~ ΔCFB.
Solution and Explanation
Given: ABCD is a parallelogram, where BE intersects CD at F. E is a point on the side AD produced.
To Prove: ΔABE ~ ΔCFB
Proof: In ∆ABE and ∆CFB,
\(\angle\)A = \(\angle\)C (Opposite angles of a parallelogram)
\(\angle\)AEB = \(\angle\)CBF (Alternate interior angles as AE || BC)
∴ ∆ABE ∼ ∆CFB (By AA similarity criterion)
Hence Proved
Top Questions on Triangles
In the adjoining figure, \(PQ \parallel XY \parallel BC\), \(AP=2\ \text{cm}, PX=1.5\ \text{cm}, BX=4\ \text{cm}\). If \(QY=0.75\ \text{cm}\), then \(AQ+CY =\)
- Assertion (A) : \(\triangle ABC \sim \triangle PQR\) such that \(\angle A = 65^\circ\), \(\angle C = 60^\circ\). Hence \(\angle Q = 55^\circ\).
Reason (R) : Sum of all angles of a triangle is \(180^\circ\). - If the orthocentre of the triangle formed by the lines $ y = x + 1 $, $ y = 4x - 8 $, and $ y = mx + c $ is at $ (3, -1) $, then $ m - c $ is:
In the adjoining figure, \( \triangle CAB \) is a right triangle, right angled at A and \( AD \perp BC \). Prove that \( \triangle ADB \sim \triangle CDA \). Further, if \( BC = 10 \text{ cm} \) and \( CD = 2 \text{ cm} \), find the length of } \( AD \).
If a line drawn parallel to one side of a triangle intersecting the other two sides in distinct points divides the two sides in the same ratio, then it is parallel to the third side. State and prove the converse of the above statement.
Questions Asked in CBSE X exam
Leaves of the sensitive plant move very quickly in response to ‘touch’. How is this stimulus of touch communicated and explain how the movement takes place?
- CBSE Class X - 2025
- Plant Biology
- Rama is a farmer. She needs loan for agriculture work. Which of the following sources of loan will be beneficial for Rama? Choose the most appropriate option:
I. Bank
II. Agricultural Trader
III. Self-Help Group
IV. Government- CBSE Class X - 2025
- Money and Credit
Read the following sources of loan carefully and choose the correct option related to formal sources of credit:
(i) Commercial Bank
(ii) Landlords
(iii) Government
(iv) Money Lende- CBSE Class X - 2025
- Money and Credit
- Two statements are given below. They are Assertion (A) and Reason (R). Read both the statements carefully and choose the correct option. Assertion (A): Rupees is accepted as medium of exchange in India.
Reason (R): The World Bank legalises the use of rupee as a medium of payment in India.- CBSE Class X - 2025
- Money and Credit
- Rama is a farmer. She needs loan for agriculture work. Which of the following sources of loan will be beneficial for Rama? Choose the most appropriate option. I. Bank
II. Agricultural Trader
III. Self-Help Group
IV. Government- CBSE Class X - 2025
- Money and Credit