abcd is a square. find the lengths of all sides to justify that they are congruent. use the distance formula or the pythagorean theorem.

write your answer in the form sqrt(____) with no spaces.

ab =
bc =
cd =
da =

all four sides have the same length.

Question

abcd is a square. find the lengths of all sides to justify that they are congruent. use the distance formula or the pythagorean theorem.

write your answer in the form sqrt(____) with no spaces.

ab =
bc =
cd =
da =

all four sides have the same length.

Accepted Answer

{ "quality": "clear", "question_count": 4, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Pythagorean Theorem Application" ], "new_concepts": [ "Distance Formula in Coordinate Geometry" ], "current_concepts": [ "Pythagorean Theorem Application", "Distance Formula in Coordinate Geometry" ] } ## Calculate the length of AB $$ \begin{aligned} A(2,4),&\quad B(5,3)\ AB &= \sqrt{(5-2)^2 + (3-4)^2}\ &= \sqrt{3^2 + (-1)^2}\ &= \sqrt{9 + 1}\ &= \sqrt{10} \end{aligned} $$ ## Calculate the length of BC $$ \begin{aligned} B(5,3),&\quad C(4,0)\ BC &= \sqrt{(4-5)^2 + (0-3)^2}\ &= \sqrt{(-1)^2 + (-3)^2}\ &= \sqrt{1 + 9}\ &= \sqrt{10} \end{aligned} $$ ## Calculate the lengths of CD and DA $$ \begin{aligned} C(4,0),&\quad D(1,1), \quad A(2,4)\ CD &= \sqrt{(1-4)^2 + (1-0)^2} = \sqrt{(-3)^2 + 1^2} = \sqrt{10}\ DA &= \sqrt{(2-1)^2 + (4-1)^2} = \sqrt{1^2 + 3^2} = \sqrt{10} \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 1 | $AB =$ | sqrt(10) | | 2 | $BC =$ | sqrt(10) | | 3 | $CD =$ | sqrt(10) | | 4 | $DA =$ | sqrt(10) | { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula in Coordinate Geometry" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the length of AB

Calculate the length of BC

Calculate the lengths of CD and DA

Answer:

No.	Problem	Answer
2	\(BC =\)	sqrt(10)
3	\(CD =\)	sqrt(10)
4	\(DA =\)	sqrt(10)