In Fig. 6.29, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS. State whether the statement is true or false.
Solution:
Given, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS.
We have to determine if the given statement is true or false.
Considering triangle ADB and ACD,
Since AD ⊥ BC, BD = DC
∠ADB = ∠ADC = 90°
Common side = AD
AD is the bisector of angle BAC.
∠BAD = ∠CAD
ASA congruence criterion states that, "if two angles of one triangle, and the side contained between these two angles, are respectively equal to two angles of another triangle and the side contained between them, then the two triangles will be congruent".
By ASA rule, ∆ABD ≅ ∆ACD
Therefore, ∆ABD and ∆ACD are not congruent by RHS.
✦ Try This: In a triangle PQR, PQ ⊥ QR and PS is the bisector of angle QPR. Then, ∆PQR ≅ ∆PRS by AAS. State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 106
In Fig. 6.29, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS. State whether the statement is true or false.
Summary:
The given statement,”In Fig. 6.29, AD ⊥ BC and AD is the bisector of angle BAC. Then, ∆ABD ≅ ∆ACD by RHS” is false.
☛ Related Questions: