question 31 of 40

if $ \overline{ad} \cong \overline{bd} $, which of the following relationships can be proved and why?

a. there is not enough information to prove a relationship.
b. $ \delta acd \cong \delta bcd $, because of as.
c. $ \delta acd \cong \delta bcd $, because of asa.
d. $ \delta acd \cong \delta bcd $, because of sas.

Question

question 31 of 40

if $ \overline{ad} \cong \overline{bd} $, which of the following relationships can be proved and why?

a. there is not enough information to prove a relationship.
b. $ \delta acd \cong \delta bcd $, because of as.
c. $ \delta acd \cong \delta bcd $, because of asa.
d. $ \delta acd \cong \delta bcd $, because of sas.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Reflexive Property of Congruence", "Triangle Congruence Postulates" ], "new_concepts": [], "current_concepts": [ "Reflexive Property of Congruence", "Triangle Congruence Postulates" ] } ## Identify given congruent parts $$ \begin{aligned} &\overline{AD} \cong \overline{BD} \quad \text{(Given)} \ &\angle ADC \cong \angle BDC = 90^\circ \quad \text{(Perpendicular lines from diagram)} \end{aligned} $$ ## Apply reflexive property $$ \overline{CD} \cong \overline{CD} \quad \text{(Reflexive Property)} $$ ## Determine triangle congruence postulate $$ \begin{aligned} &\text{Side: } \overline{AD} \cong \overline{BD} \ &\text{Included Angle: } \angle ADC \cong \angle BDC \ &\text{Side: } \overline{CD} \cong \overline{CD} \ &\therefore \Delta ACD \cong \Delta BCD \quad \text{(SAS Postulate)} \end{aligned} $$

A. There is not enough information to prove a relationship.

B. $\Delta ACD \cong \Delta BCD$, because of AS.

C. $\Delta ACD \cong \Delta BCD$, because of ASA.

D. $\Delta ACD \cong \Delta BCD$, because of SAS.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Triangle Congruence Postulates" ] }

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QUESTION IMAGE

Question

Explanation:

Identify given congruent parts

Apply reflexive property

Determine triangle congruence postulate

Answer: