Question

9. In figure, ABC is a triangle in which D is mid point of AB. If DM I AC , DN 1 BC and
DM=DN, prove that AC=BC.
​

Answer 1

Step-by-step explanation:

What would you like to ask?

10th

Maths

Triangles

Criteria for Triangle Similarity

D is the mid point of the b...

MATHS

D is the mid point of the base BC of a triangle ABC. DM and DN are perpendiculars on AB and AC respectively. If DM=DN, the triangle is

EASY

Share

Study later

ANSWER

Given: D is mid point of BC. DM⊥AB and DN⊥AC, DM=DN

Now, In △DMB and △DNC,

DM=DN (Given)

∠DMB=∠DNC (Each 90

∘

)

BD=DC (D is mid point of BC)

Thus, △DMB≅△DNC (SAS rule)

Thus, ∠B=∠C (By cpct)

hence, △ABC is an Isosceles triangle.