Mathematics
In △ABC, AB > AC and D is any point on BC, then, AB is :
< DC
< AD
= BC
> AD
Triangles
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Answer
In △ABC,
We know that,
The larger angle of a triangle has the longer side opposite to it.
⇒ AB > AC
⇒ ∠ACB > ∠ABC ….(1)
From figure,
⇒ ∠ADB > ∠ACD (exterior angle of a triangle is greater than interior opposite angle)
⇒ ∠ADB > ∠ACB ….(2)
From eq.(1) and (2), we have:
⇒ ∠ADB > ∠ABC
⇒ ∠ADB > ∠ABD
⇒ AB > AD (larger angle of a triangle has the larger side opposite to it).
Hence, option 4 is the correct option.
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Case Study
Ms Anu Gupta teaches mathematics to class 9 in a school. One day she drew a figure on the board in the class. She provided the following clues to the students.
AB || CD
O is the mid-points of AD
Based on this information, answer the following questions:
△OAB ≅ △ODC by which of the following congruent condition?
(a) SAS
(b) ASA
(c) SSS
(d) RHS∠AOB = ∠DOC holds because:
(a) Alternate angles are equal
(b) Corresponding angles are equal
(c) Vertically opposite angles are equal
(d) None of theseWhich of the following is correct?
(a) ∠A = ∠C
(b) ∠B = ∠D
(c) ∠B = ∠C
(d) ∠AOB = ∠OCBWhich of the following is correct?
(a) AO = OB
(b) AB = OB
(c) OD = CD
(d) OC = OBWhich of the following is not a congruent condition?
(a) ASA
(b) SSS
(c) AAA
(d) AAS
Assertion (A): The orthocentre of a triangle may lie in the exterior of the triangle.
Reason (R): The point of intersection of the medians of a triangle is called its orthocentre.
A is true, R is false
A is false, R is true
Both A and R are true
Both A and R are false