Complete the following proof related to the figure below.

given:
a, b are rt 's
ac = bd

prove:
mc = md

which of the following could not be used as the reason in line 3 of the proof?

hl
la
aas

HL

Step-by-step explanation:

We are given that

We have to find the postulate that is not used in line 3 reason in given proof.

In triangle MAC and BMD

Statement:

Reason: Given

Statement:

Reason: Vertical opposite angle theorem

Statement:

Reason: AAS Postulate or LA postulate

AAS postulate: When two angles and one side of one triangle is equal to two corresponding angles and corresponding side of other triangle .Then , two triangles are congruent by AAS postulate.

LA postulate: When one acute angle and  one leg of one triangle is equal to its corresponding angle and corresponding leg of other triangle .Then, two triangles are congruent by LA postulate.

HL Postulate: When hypotenuse and one leg of one triangle is equal to its corresponding hypotenuse and corresponding leg of other triangle .Then, two triangles are congruent by HL postulate.

But we are not given MC=BM

Therefore, we cannot use HL postulate.

Statement:

Reason:CPCT

step-by-step explanation:

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,