Advertisements
Advertisements
प्रश्न
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
(iii) AC bisects angle DCB
Advertisements
उत्तर
Given: In the figure,
AB = AD, CB = CD
To prove: Δ ABC ≅ Δ ADC
∠B = ∠D
AC bisects angle DCB
Proof: In Δ ABC and Δ ADC,
AC = AC .............(common)
AB = AD .............(given)
CB = CD .............(given)
(i) ∴ Δ ABC ≅ Δ ADC .................(SSS aciom)
(ii) ∴ ∠B = D .................(c.p.c.t.)
∠BCA = ∠DCA
(iii) ∴ AC bisects ∠DCB
APPEARS IN
संबंधित प्रश्न
If ΔABC ≅ ΔABC is isosceles with
ΔPQR and ΔABC is not congruent to ΔRPQ, then which of the following is not true:
In the given figure, the measure of ∠B'A'C' is
In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.
AD and BE are altitudes of an isosceles triangle ABC with AC = BC. Prove that AE = BD.
In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.
In the figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the mid-point of the line segments AB and PQ.
ΔABC is isosceles with AB = AC. BD and CE are two medians of the triangle. Prove that BD = CE.
ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.
Prove that
(i) BG = CH
(ii) AG = AH
Is it possible to construct a triangle with lengths of its sides as 4 cm, 3 cm and 7 cm? Give reason for your answer.
