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प्रश्न
In triangles ABC and CDE, if AC = CE, BC = CD, ∠A = 60°, ∠C = 30° and ∠D = 90°. Are two triangles congruent?
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उत्तर
For the triangles ABC and ECD, we have the following information and corresponding figure:
AC = CE
BC = CD
∠A = 60°
∠C = 30°
∠D = 90°
In triangles ABC and ECD, we have
AC = EC
BC = CD
and ∠BAC= ∠CED
The SSA criteria for two triangles to be congruent are being followed. So both the triangles are congruent.
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संबंधित प्रश्न
Line l is the bisector of an angle ∠A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠A (see the given figure). Show that:
- ΔAPB ≅ ΔAQB
- BP = BQ or B is equidistant from the arms of ∠A.
You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.
| Steps | Reasons | ||
| 1 | PM = QM | 1 | ... |
| 2 | ∠PMA = ∠QMA | 2 | ... |
| 3 | AM = AM | 3 | ... |
| 4 | ΔAMP ≅ ΔAMQ | 4 | ... |
In Fig. 10.92, it is given that AB = CD and AD = BC. Prove that ΔADC ≅ ΔCBA.
In the given figure, prove that:
CD + DA + AB + BC > 2AC
In two congruent triangles ABC and DEF, if AB = DE and BC = EF. Name the pairs of equal angles.
ABC is an isosceles triangle in which AB = AC. BE and CF are its two medians. Show that BE = CF.
In the following figure, BL = CM.
Prove that AD is a median of triangle ABC.
In the parallelogram ABCD, the angles A and C are obtuse. Points X and Y are taken on the diagonal BD such that the angles XAD and YCB are right angles.
Prove that: XA = YC.
In the following figure, OA = OC and AB = BC.
Prove that: ΔAOD≅ ΔCOD
In the following figure, ABC is an equilateral triangle in which QP is parallel to AC. Side AC is produced up to point R so that CR = BP.
Prove that QR bisects PC.
Hint: ( Show that ∆ QBP is equilateral
⇒ BP = PQ, but BP = CR
⇒ PQ = CR ⇒ ∆ QPM ≅ ∆ RCM ).
