determining similarity of two triangles

3. compare corresponding sides that include the corresponding, congruent angles to show they are in proportion.
$\frac{ab}{ad}$ is equal to dropdown
$\frac{ac}{ae}$ is equal to dropdown

Question

determining similarity of two triangles

3. compare corresponding sides that include the corresponding, congruent angles to show they are in proportion.
$\frac{ab}{ad}$ is equal to dropdown
$\frac{ac}{ae}$ is equal to dropdown

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Coordinate Geometry" ], "new_concepts": [ "Triangle Similarity", "Side-Angle-Side Similarity" ], "current_concepts": [ "Distance Formula", "Coordinate Geometry", "Triangle Similarity", "Side-Angle-Side Similarity" ] } ## Calculate lengths of AB and AD $$ \begin{aligned} A &= (3, 1), \quad B = (1, 4), \quad D = (-1, 7) \ AB &= \sqrt{(1 - 3)^2 + (4 - 1)^2} = \sqrt{(-2)^2 + 3^2} = \sqrt{4 + 9} = \sqrt{13} \ AD &= \sqrt{(-1 - 3)^2 + (7 - 1)^2} = \sqrt{(-4)^2 + 6^2} = \sqrt{16 + 36} = \sqrt{52} = 2\sqrt{13} \ \frac{AB}{AD} &= \frac{\sqrt{13}}{2\sqrt{13}} = \frac{1}{2} \end{aligned} $$ ## Calculate lengths of AC and AE $$ \begin{aligned} A &= (3, 1), \quad C = (5, 3), \quad E = (7, 5) \ AC &= \sqrt{(5 - 3)^2 + (3 - 1)^2} = \sqrt{2^2 + 2^2} = \sqrt{8} = 2\sqrt{2} \ AE &= \sqrt{(7 - 3)^2 + (5 - 1)^2} = \sqrt{4^2 + 4^2} = \sqrt{32} = 4\sqrt{2} \ \frac{AC}{AE} &= \frac{2\sqrt{2}}{4\sqrt{2}} = \frac{1}{2} \end{aligned} $$ 3. Compare corresponding sides that include the corresponding, congruent angles to show they are in proportion. $\frac{AB}{AD}$ is equal to $\frac{1}{2}$ $\frac{AC}{AE}$ is equal to $\frac{1}{2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Similarity" ] }

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Calculate lengths of AB and AD

Calculate lengths of AC and AE

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