Question

What is the flaw in the student's proof?
Justification 3 should be "Angle ABC = Angle BAD and Angle BAC = Angle ABD."

Justification 4 should be "AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD."

Justification 2 should be "BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC."

Justification 1 should be "Angle ABC = Angle BCD and Angle BCA = Angle DBC."

Answer 1

@mathstudent55 will you help me ?

Answer 2

I'm going over it now.

Answer 3

Look at step 1.
How do you prove two triangles similar using angles?

Answer 4

@mathstudent55 2 angles most be congruent

Answer 5

Right. Look at step 1. There are two angles of triangle shown to be congruent to two angles of triangle BDC. That means statement 1 and justification 1 are both correct.

Answer 6

Now let's look at step 2.

Answer 7

@mathstudent55 i dont get step 2 ....

Answer 8

@mathstudent55 will you explain ?

Answer 9

@Miyuru will you help ?

Answer 10

Ok. Let's go over step 2 together.

Answer 11

Look at justification 2.

Answer 12

I am also confused on how BC^2 = AC x DC :(

Answer 13

yeah right ! @Miyuru actually i think the mess is in the second one !

Answer 14

I figured it out. Just follow along.

This is justification 2:
BC/DC = BC/AC

Answer 15

When you have similar triangles, the lengths of the sides are proportional

Answer 16

Let's look at the sides to see of this proportion is correct.

Answer 17

In the figure above, I separated the two triangles to show them in an easier to understand way.

Answer 18

We have to look for the one that is wrong !

Answer 19

Now I repositioned the smaller triangle to see more clearly the corresponding sides of the two similar triangles.