Sovi AI

Question

Solution Steps

1. Understand the question

   ving for a missing side.
   -overlapping triangles and creating equ
   -altitude problems
   -area and perimeter
   additional review topic:
   triangle inequality
   trigonometry
   part 1: similar triangle definitions
   in the accompanying diagram of right triangle abc,
   altitude \\(\\overline{bd}\\) is drawn to hypotenuse \\(\\overline{ac}\\)
   which statement must always be true?

   1. \\(\\frac{ad}{ab} = \\frac{bc}{ac}\\)
   2. \\(\\frac{ad}{ab} = \\frac{ab}{ac}\\)
   3. \\(\\frac{bd}{bc} = \\frac{ab}{ad}\\)
   4. \\(\\frac{ab}{bc} = \\frac{bd}{ac}\\)
2. Explanation

   Step1: Identify Similar Triangles

   In right triangle \( ABC \) with altitude \( BD \) to hypotenuse \( AC \), we have three similar triangles: \( \triangle ABC \sim \triangle ADB \sim \triangle BDC \) (by AA similarity, as all right triangles and share a common angle).

   Step2: Corresponding Sides of Similar Triangles

   For similar triangles \( \triangle ADB \) and \( \triangle ABC \), the ratios of corresponding sides are equal.

   • In \( \triangle ADB \), sides are \( AD \) (adjacent to \( \angle A \)), \( AB \) (hypotenuse), and \( BD \) (opposite to \( \angle A \)).
   • In \( \triangle ABC \), sides are \( AB \) (adjacent to \( \angle A \)), \( AC \) (hypotenuse), and \( BC \) (opposite to \( \angle A \)).

   So, the ratio of \( AD \) (from \( \triangle ADB \)) to \( AB \) (from \( \triangle ADB \)) should equal the ratio of \( AB \) (from \( \triangle ABC \)) to \( AC \) (from \( \triangle ABC \)) because they are corresponding sides of similar triangles. Mathematically, this is \( \frac{AD}{AB} = \frac{AB}{AC} \).

   Step3: Analyze Other Options

   • Option 1: \( \frac{AD}{AB} = \frac{BC}{AC} \) – \( BC \) and \( AD \) are not corresponding sides, so this is incorrect.
   • Option 3: \( \frac{BD}{BC} = \frac{AB}{AD} \) – Sides do not correspond, so incorrect.
   • Option 4: \( \frac{AB}{BC} = \frac{BD}{AC} \) – Sides do not correspond, so incorrect.
3. Final answer
   1. \( \boldsymbol{\frac{AD}{AB} = \frac{AB}{AC}} \)

Answer

Question Analysis

OCR Text

ving for a missing side.
-overlapping triangles and creating equ
-altitude problems
-area and perimeter
additional review topic:
triangle inequality
trigonometry
part 1: similar triangle definitions
in the accompanying diagram of right triangle abc,
altitude \\(\\overline{bd}\\) is drawn to hypotenuse \\(\\overline{ac}\\)
which statement must always be true?
1) \\(\\frac{ad}{ab} = \\frac{bc}{ac}\\)
2) \\(\\frac{ad}{ab} = \\frac{ab}{ac}\\)
3) \\(\\frac{bd}{bc} = \\frac{ab}{ad}\\)
4) \\(\\frac{ab}{bc} = \\frac{bd}{ac}\\)

Related Topics

Related Questions

• use an area model to solve 31 × 26. multiply in the area model.

  Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806

• 6. solve each equation. write each solution as a fraction and as a deci…

  | Equation | Solution (Fraction) | Solution (Decimal) | |----------|---------------------|--------------------| | $2x=3$ | $\frac{3}{2}$ | $1.5$ | | $5y=3$ | $\frac{3}{5}$ | $0.6$…

• Ok

  - Fila 2: Circular el par (5, 2). - Fila 3: Circular el par (3, 3) (o la tarjeta con 3 y la otra con 4 dibujos, pero los números son 3 y 3? Wait, la tercera fila: primera tarjeta …

• How do you solve pemdas

  It's basically just a checklist so you don't get mixed up when a math problem has a bunch of stuff going on at once. You just go down the list in order: 1. **P**arentheses: Do any…

• which number line models $-1 + (-14)$? add. $-1 + (-14) = \\square$

  \(-15\)

• 11 et 12

  The initial number of bacteria is 5. ### Turn 2 Answer Ça marche, regardons ça ! On dirait que tu es en plein dans les maths financières. Pour le **numéro 11**, on cherche le taux…

• calculate the area and perimeter(all around). perimeter: ____ ft area: …

  Perimeter: 112 ft Area: 488 ft²

• find the vertex of the parabola ( y = x^2 ). simplify both coordinates …

  \((0, 0)\)

Sovi AI iOS

Official website: mysovi.ai. Question pages are served on question-banks.mysovi.ai. iOS app is distributed through the Apple App Store.