Advertisements
Advertisements
Question
In the given figure ray AZ bisects ∠BAD and ∠DCB, prove that AB = AD
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
By applying the ASA congruence rule, it is to be established that ∆ABC ≅ ∆QRP and it is given that BC = RP. What additional information is needed to establish the congruence?
In the given figure, AC ≡ AD and ∠CBD ≡ ∠DEC. Prove that ∆BCF ≡ ∆EDF.
State whether the two triangles are congruent or not. Justify your answer
For the given pair of triangles state the criterion that can be used to determine the congruency?
Two triangles are congruent, if two angles and the side included between them in one of the triangles are equal to the two angles and the side included between them of the other triangle. This is known as the ______.
In the given figure, ∆ARO ≅ ∆______.
In the given 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.
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?
