Advertisements
Advertisements
Question
In the given figure ray AZ bisects ∠BAD and ∠DCB, prove that AB = AD
Advertisements
Solution
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
RELATED QUESTIONS
In Fig, can you use the ASA congruence rule and conclude that ∆AOC ≅ ∆BOD?
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:
In the figure, ∠TMA ≡∠IAM and ∠TAM ≡ ∠IMA. P is the midpoint of MI and N is the midpoint of AI. Prove that ΔPIN ~ ΔATM
To conclude the congruency of triangles, mark the required information in the following figure with reference to the given congruency criterion
For the given pair of triangles state the criterion that can be used to determine the congruency?
If hypotenuse and an acute angle of one right triangle are equal to the hypotenuse and an acute angle of another right triangle, then the triangles are congruent.
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.
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?
