Question

Given triangle abc which of the following must be true

Answer 1

I, II, and III are all correct.

Answer 2

The correct statements are:

I, II , III

Explanation:

• In the given triangle i.e. ΔABC we have:

length of side AB= length of side AC= 20 units

Hence, we have:

∠B≅∠C

( since the angle opposite to equal side are equal )

• Also, we see that the line AD is perpendicular to side BC.

Hence, we have:

∠BDA≅∠CDA

( Since both the angles have equal measure )

• Hence, as two angles of a triangle are congruent to each other so the third angle will also be congruent.

( Since m∠B=m∠C

and m∠ADB=m∠ADC

⇒ m∠B+m∠ADB=m∠C+m∠ADC--------------(1)

By triangle sum theorem we have:

In ΔADB

m∠B+m∠ADB+m∠DAB=180°

⇒ m∠DAB=180°-(m∠B+m∠ADB)

and in ΔADC by triangle sum theorem we have:

m∠DAC=180°-(m∠C+m∠ADC)

Hence, by equation (1) we have:

m∠DAB=m∠CAD )