Question

"A student made the following chart to prove that AB2 + BC2 = AC2.

Answer 1

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 $\triangle ABC$ and $\triangle BDC$  

$\angle BAC = \angle DBC \\\angle ACB = \angle BCD$

All the angles of triangle are equal.

∴$\triangle ABC \sim \triangle BDC$

Since, $\triangle ABC \sim \triangle BDC$

$\frac{AC}{BC}=\frac{AC}{DC}$

$BC^{2}=AC \times DC$

In $\triangle ABC$ and $\triangle BDA$,

$\fbox{\begin\\ \angle ABC= \angle BDA = 90^{\circ}\end{minispace}}$

$\fbox{\begin \\\angle BAC = \angle BAD\\\end{minispace}}$

$\angle ACB = \angle ABD$

All the angles of triangle are equal.

∴$\fbox{\begin\triangle ABC \sim \triangle BDA \end{minispace}}$

∵$\triangle ABC \sim \triangle BDA$  

$\frac{AC}{AB}=\frac{AB}{AD}$

$AB^{2}=AC \times AD$

Now, $AB^{2}+BC^{2}$ can be simplified as,

$AB^{2}+BC^{2}=AC \times AD+AC \times DC\\AB^{2}+BC^{2}=AC(AD+DC)\\AB^{2}+BC^{2}=AC(AC)\\AB^{2}+BC^{2}=AC^{2}$

Learn more:

1. Find the height of the triangle?

brainly.com/question/12989306

2. Which undefined term is needed to define an angle? brainly.com/question/3717797

3. Look at the figure, which trigonometric ratio should you use to find x? brainly.com/question/9880052

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