Advertisements
Advertisements
प्रश्न
In the given figure ray AZ bisects ∠BAD and ∠DCB, prove that AB = AD
Advertisements
उत्तर
In ∆BAC and ∆DAC
∠BAC = ∠DAC ...[Given `bar("AZ")` bisects ∠BAD]
∠BCA = ∠DCA ...[`bar("AZ")` bisects ∠DCB]
AC = AC ...[∵ common side]
∴ Here AC is the included side of the angles
By ASA criterior, ∆BAC ≅ ∆DAC .......(i)
From (i) ∆BAC ≅ ∆DAC
BA = DA ...[By CPCTC]
i.e., AB = AD
APPEARS IN
संबंधित प्रश्न
Given below are measurements of some parts of two triangles. Examine whether the two triangles are congruent or not, by the ASA congruence rule. In the case of congruence, write it in symbolic form.
∆DEF, ∠D = 60º, ∠F = 80º, DF = 6 cm.
∆PQR, ∠Q = 60º, ∠R = 80º, QP = 6 cm.
Consider the given pairs of triangles and say whether each pair is that of congruent triangles. If the triangles are congruent, say ‘how’; if they are not congruent say ‘why’ and also say if a small modification would make them congruent:
ΔABC and ΔDEF are two triangles in which AB = DF, ∠ACB = 70°, ∠ABC = 60°, ∠DEF = 70° and ∠EDF = 60°. Prove that the triangles are congruent
State whether the two triangles are congruent or not. Justify your answer
To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion
In the given figure ray AZ bisects ∠BAD and ∠DCB, prove that ∆BAC ≅ ∆DAC
In the following figure, ∆ARO ≅ ∆ ______.
In the following figure, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS.
In the given pairs of triangles of figure, applying only ASA congruence criterion, determine which triangles are congruent. Also, write the congruent triangles in symbolic form.
Observe the given figure and state the three pairs of equal parts in triangles ABC and DBC.
- Is ∆ABC ≅ ∆DCB? Why?
- Is AB = DC? Why?
- Is AC = DB? Why?
