according to the diagram below, which similarity statements are true?

check all that apply.

a. $\delta abc \sim \delta adc$
b. $\delta abc \sim \delta adb$
c. $\delta abc \sim \delta bdc$
d. $\delta abd \sim \delta bcd$

Question

according to the diagram below, which similarity statements are true?

check all that apply.

a. $\delta abc \sim \delta adc$
b. $\delta abc \sim \delta adb$
c. $\delta abc \sim \delta bdc$
d. $\delta abd \sim \delta bcd$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Similar Right Triangles" ], "new_concepts": [], "current_concepts": [ "Similar Right Triangles", "AA Similarity Postulate" ] } ## Identify the given geometric properties Using the *Similar Right Triangles* knowledge point $$ \begin{aligned} &\angle ABC = 90^\circ\ &BD \perp AC \implies \angle ADB = \angle BDC = 90^\circ \end{aligned} $$ ## Establish similarity between the triangles Using the *Similar Right Triangles* knowledge point $$ \begin{aligned} &\triangle ABC \sim \triangle ADB \quad (\text{sharing } \angle A \text{ and right angles})\ &\triangle ABC \sim \triangle BDC \quad (\text{sharing } \angle C \text{ and right angles})\ &\triangle ADB \sim \triangle BDC \quad (\text{transitive property of similarity}) \end{aligned} $$ ## Evaluate the given options Using the *Similar Right Triangles* knowledge point $$ \begin{aligned} &\text{Option A: } \triangle ABC \sim \triangle ADC \quad (\text{False, } \triangle ADC \text{ is not a right triangle})\ &\text{Option B: } \triangle ABC \sim \triangle ADB \quad (\text{True})\ &\text{Option C: } \triangle ABC \sim \triangle BDC \quad (\text{True})\ &\text{Option D: } \triangle ABD \sim \triangle BCD \quad (\text{True}) \end{aligned} $$

A. $\triangle ABC \sim \triangle ADC$

B. $\triangle ABC \sim \triangle ADB$

C. $\triangle ABC \sim \triangle BDC$

D. $\triangle ABD \sim \triangle BCD$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Similar Right Triangles" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the given geometric properties

Establish similarity between the triangles

Evaluate the given options

Answer: