Advertisements
Advertisements
प्रश्न
In the following diagram, ABCD is a square and APB is an equilateral triangle.
(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.
Advertisements
उत्तर
Given: ABCD is a Square and ΔAPB is an equilateral triangle.
We need to
(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC
Proof:
Since AB side is present in both square & equilateral triangle
AP = PB = AB =AD = CD = BC
(i) In ΔBPC,
BP = BC
∴ ∠BPC = ∠PCB
∠BPC + ∠PCB + 30° = 180°
∠BPC + ∠BPC = 150°
2∠BPC = ` (150°)/2 = 75°`
∴ ∠BPC = ∠PCB = 75°
∠ADP = ∠DPA = 75° ...[C.P.C.T.C]
(ii) In DPC
∠DCP = 90° - 75° = 15°
∠PDC = 90° - 75° = 15°
∠DPC = 180° - (15° + 15°)
∠DPC = 150°
APPEARS IN
संबंधित प्रश्न
In triangles ABC and PQR, if ∠A = ∠R, ∠B = ∠P and AB = RP, then which one of the following congruence conditions applies:
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.
In the adjacent figure, seg AD ≌ seg EC Which additional information is needed to show that ∆ ABD and ∆ EBC will be congruent by A-A-S test?
If the following pair of the triangle is congruent? state the condition of congruency:
In ΔABC and ΔPQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.
State, whether the pairs of triangles given in the following figures are congruent or not:
Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).
In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.
In the figure, RT = TS, ∠1 = 2∠2 and ∠4 = 2∠3. Prove that ΔRBT ≅ ΔSAT.
In ΔABC, AD is a median. The perpendiculars from B and C meet the line AD produced at X and Y. Prove that BX = CY.
The top and bottom faces of a kaleidoscope are congruent.
