"a student made the following chart to prove that ab2 + bc2 = ac2.

statement justification
1. triangle abc is similar to triangle bdc 1. angle abc = angle bdc and angle bca = angle bcd
2. bc2 = ac × dc 2. bc ÷ dc = ac ÷ bc because triangle abc is similar to triangle bdc
3. triangle abc is similar to triangle abd 3. angle abc = angle bad and angle bac = angle abd
4. ab2 = ac × ad 4. ab ÷ ad = ac ÷ ab because triangle abc is similar to triangle abd
5. ab2 + bc2 = ac × ad + ac × dc
= ac (ad + dc)
6. adding statement 1 and statement 2
7. ab2 + bc2 = ac2

which of the first four steps is the error? "

Step 3 has an error.

Step-by-step explanation:

Similarity-criteria of triangles:

1.All the corresponding angles of two triangles should be equal.

2.The ratio between the corresponding sides of two triangles should be equal.

In and  

All the angles of triangle are equal.

∴

Since,

In and ,

All the angles of triangle are equal.

∴

∵  

Now, can be simplified as,

Learn more:

1.Find the height of the triangle?

link

2.Which undefined term is needed to define an angle? link

3.Look at the figure, which trigonometric ratio should you use to find x? link

Answer Details

Grade: Junior High School

Subject: Mathematics

Chapter: Triangle

Keywords: triangle, similar, similarity, ratio of sides, right triangle, similar triangle, ratio of sides, equal angles, square of hypotenuse, sum, square of legs, sum of square of legs

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