Question

Given: △ABC, D∈ AC m∠ABC=m∠BDA AB=2, AC=4 Find: AD and DC

Answer 1

AD = 1

DC = 3

Explanation:

First, we know that ∠ABC = ∠BDA, because it is stated in the problem. We also know that ∠A = ∠A, because that angle is common in both angles. To better visualize this, there is a picture below. Therefore, ΔABC is similar to ΔBDA. We are also aware of the fact that AB = 2, and AC = 4. Therefore, the ratio of similitude is 1:2.

Since the two triangles are similar, side AB is proportionate to side AC, side AD is proportionate to side AB, and side BD is proportionate to side BC.

Using this fact and the ratio of similitude, we can write the following ratio:

AD:AB = 1:2

We can substitute 2 for AB in this ratio, and we find that AD = 1.

Since AD + DC = AC, and AC = 4, DC = 3.

Answer 2

The value of AD=1 and DC=3

Explanation:

Given: ΔABC, D∈ AC m∠ABC=m∠BDA, AB=2, AC=4

Diagram: Please find attachment.

To find: AD=? and DC=?

Calculation:

In ΔABC and ΔADB

∠ABC=∠ADB (Given)

∠A=∠A (Common)

Therefore, ΔABC ≈ ΔADB by AA similarity

If two triangles are similar then ratio their corresponding sides are equal

Therefore,

`(AD)/(AB)=(AB)/(AC)`

where, AD=?, AB=2, AC=4

`(AD)/(2)=(2)/(4)`

`AD=(2* 2)/(4)=1`

AD=1

AD+DC=AC

1+DC=4

DC=4-1

DC=3

Hence, The value of AD=1 and DC=3