Advertisements
Advertisements
Question
In the given figure, AB ⊥ BE and FE ⊥ BE. If BC = DE and AB = EF, then ΔABD is congruent to
Options
ΔEFC
ΔECF
ΔCEF
ΔFEC
Advertisements
Solution
ΔFEC
Explanation:
It is given that
In the figure, AB ⊥ BE, FE ⊥ BE
Now, BC = DE.
Adding DC to both the sides, we get,
⇒ BC + DC = DE + DC
⇒ BD = CE
In ΔABD and ΔCEF
BD = CE (Proved)
AB = FE (Given)
∠ABD = ∠FEC (Each 90°)
∴ ΔABD ≅ ΔFEC by SAS congruence rule.
APPEARS IN
RELATED QUESTIONS
In the given figure, if AB = AC and ∠B = ∠C. Prove that BQ = CP.
In the given figure, if AE || DC and AB = AC, the value of ∠ABD is
In ΔTPQ, ∠T = 65°, ∠P = 95° which of the following is a true statement?
In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.
The following figure has shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.
Prove that: (i) AM = AN (ii) ΔAMC ≅ ΔANB
State, whether the pairs of triangles given in the following figures are congruent or not:
State, whether the pairs of triangles given in the following figures are congruent or not:
Δ ABC in which AB = 2 cm, BC = 3.5 cm and ∠C = 80° and Δ DEF in which DE = 2 cm, DF = 3.5 cm and ∠D = 80°.
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 70°,BC = 6cm,∠C = 50°);
ΔXYZ;(∠Z = 60°,XY = 6cm,∠X = 70°).
In ΔABC, X and Y are two points on AB and AC such that AX = AY. If AB = AC, prove that CX = BY.
In triangles ABC and DEF, AB = FD and ∠A = ∠D. The two triangles will be congruent by SAS axiom if ______.
