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
In Fig. 10.22, the sides BA and CA have been produced such that: BA = AD and CA = AE.
Prove that segment DE || BC.
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 triangles in each pair are congruent.
By ______ test
ΔPRQ ≅ ΔSTU
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?
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.
State, whether the pairs of triangles given in the following figures are congruent or not:
In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.
In the given figure, AB = DB and AC = DC. Find the values of x and y.
In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆PQR should be equal to side BC of ∆ABC so that the two triangles are congruent? Give reason for your answer.
“If two angles and a side of one triangle are equal to two angles and a side of another triangle, then the two triangles must be congruent.” Is the statement true? Why?
Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.
∆STU ≅ ∆DEF
