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 [tex]\triangle ABC[/tex] and [tex]\triangle BDC[/tex]
[tex]\angle BAC = \angle DBC \\\angle ACB = \angle BCD[/tex]
All the angles of triangle are equal.
∴[tex]\triangle ABC \sim \triangle BDC[/tex]
Since, [tex]\triangle ABC \sim \triangle BDC[/tex]
[tex]\frac{AC}{BC}=\frac{AC}{DC}[/tex]
[tex]BC^{2}=AC \times DC[/tex]
In [tex]\triangle ABC[/tex] and [tex]\triangle BDA[/tex],
[tex]\fbox{\begin\\ \angle ABC= \angle BDA = 90^{\circ}\end{minispace}}[/tex]
[tex]\fbox{\begin \\\angle BAC = \angle BAD\\\end{minispace}}[/tex]
[tex]\angle ACB = \angle ABD[/tex]
All the angles of triangle are equal.
∴[tex]\fbox{\begin\triangle ABC \sim \triangle BDA \end{minispace}}[/tex]
∵[tex]\triangle ABC \sim \triangle BDA[/tex]
[tex]\frac{AC}{AB}=\frac{AB}{AD}[/tex]
[tex]AB^{2}=AC \times AD[/tex]
Now, [tex]AB^{2}+BC^{2}[/tex] can be simplified as,
[tex]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}[/tex]
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
