Advertisements
Advertisements
प्रश्न
Two right-angled triangles ABC and ADC have the same base AC. If BC = DC, prove that AC bisects ∠BCD.
Advertisements
उत्तर
In ΔABC and ΔADC
∠BAC = ∠DAC ...(90°)
BC = DC
AC = AC ...(common)
Therefore, ΔABC ≅ ΔADC ...(SSA criteria)
Hence, ∠BCA = ∠DCA
Thus, AC bisects ∠BCD.
APPEARS IN
संबंधित प्रश्न
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
ΔXYZ ≅ ΔLMN
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?
The following figure 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: ΔAMC≅ ΔANB
Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D
In ΔPQR, LM = MN, QM = MR and ML and MN are perpendiculars on PQ and PR respectively. Prove that PQ = PR.
In ΔABC, X and Y are two points on AB and AC such that AX = AY. If AB = AC, prove that CX = BY.
If the perpendicular bisector of the sides of a triangle PQR meet at I, then prove that the line joining from P, Q, R to I are equal.
In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.
If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles
Which of the following rule is not sufficient to verify the congruency of two triangles
