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?
https://brainly.com/question/12989306
2. Which undefined term is needed to define an angle? https://brainly.com/question/3717797
3. Look at the figure, which trigonometric ratio should you use to find x? https://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
