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महाराष्ट्र राज्य शिक्षण मंडळएस.एस.सी (इंग्रजी माध्यम) इयत्ता ९ वी

In the given figure, seg AB ≅ seg CB and seg AD ≅ seg CD. Prove that ΔABD ≅ ΔCBD.

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प्रश्न

In the given figure, seg AB ≅ seg CB and seg AD ≅ seg CD. Prove that ΔABD ≅ ΔCBD.

बेरीज
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उत्तर

In △ABD and △CBD

seg AB = seg CB       ...(Given)

seg AD = seg CD      ...(Given)

seg BD = seg BD       ...(Common side)

△ABD ≅ △CBD          ...(SSS test)

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पाठ 3: Triangles - Practice Set 3.2 [पृष्ठ ३२]

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बालभारती Mathematics 2 [English] Standard 9 Maharashtra State Board
पाठ 3 Triangles
Practice Set 3.2 | Q 5. | पृष्ठ ३२

संबंधित प्रश्‍न

In a squared sheet, draw two triangles of equal areas such that

The triangles are congruent.

What can you say about their perimeters?


In triangles ABC and PQR three equality relations between some parts are as follows:
AB = QP, ∠B = ∠P and BC = PR

State which of the congruence conditions applies:


In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is


Which of the following is not a criterion for congruence of triangles?


In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangle in each pair are congruent.

By ______ test

ΔLMN ≅ ΔPTR


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 following diagram, ABCD is a square and APB is an equilateral triangle.

(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.


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) BN = CM (ii) ΔBMC ≅ ΔCNB   


In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.


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
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ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).


Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 5cm,BC = 7cm,CA = 9cm);
ΔKLM;(KL = 7cm,LM = 5cm,KM = 9cm).


Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(∠B = 90°,BC = 6cm,AB = 8cm);
ΔPQR;(∠Q = 90°,PQ = 6cm,PR = 10cm).


In a circle with center O. If OM is perpendicular to PQ, prove that PM = QM.


Sides, AB, BC and the median AD of ΔABC are equal to the two sides PQ, QR and the median PM of ΔPQR. Prove that ΔABC ≅ ΔPQR.


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Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.

∆ABC ≅ ∆LMN


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