what are the steps necessary to show that $\overline{jh} \cong \overline{vu}$?

check all that apply.

$vu = \sqrt{15}$

$jh = d = \sqrt{(-3 - (-5))^2 + (0 - (-3))^2}$

$vu = d = \sqrt{(5 - 2)^2 + (2 - 4)^2}$

$vw = d = \sqrt{(0 - 5)^2 + (1 - 2)^2}$

$jh = \sqrt{13}$

Question

what are the steps necessary to show that $\overline{jh} \cong \overline{vu}$?

check all that apply.

$vu = \sqrt{15}$

$jh = d = \sqrt{(-3 - (-5))^2 + (0 - (-3))^2}$

$vu = d = \sqrt{(5 - 2)^2 + (2 - 4)^2}$

$vw = d = \sqrt{(0 - 5)^2 + (1 - 2)^2}$

$jh = \sqrt{13}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Distance Formula", "Coordinate Geometry" ], "new_concepts": [], "current_concepts": [ "Distance Formula", "Coordinate Geometry", "Triangle Congruence" ] } ## Apply distance formula to JH $$ \begin{aligned} J &= (-5, -3),\quad H = (-3, 0)\ JH &= \sqrt{(-3 - (-5))^2 + (0 - (-3))^2}\ JH &= \sqrt{(2)^2 + (3)^2} = \sqrt{4 + 9} = \sqrt{13} \end{aligned} $$ ## Apply distance formula to VU $$ \begin{aligned} V &= (5, 2),\quad U = (2, 4)\ VU &= \sqrt{(5 - 2)^2 + (2 - 4)^2}\ VU &= \sqrt{(3)^2 + (-2)^2} = \sqrt{9 + 4} = \sqrt{13} \end{aligned} $$ ## Identify matching options $$ \begin{aligned} &\text{Option 2: } JH = d = \sqrt{(-3 - (-5))^2 + (0 - (-3))^2}\ &\text{Option 3: } VU = d = \sqrt{(5 - (2))^2 + (2 - 4)^2}\ &\text{Option 5: } JH = \sqrt{13} \end{aligned} $$

(A) $VU = \sqrt{15}$

(B) $JH = d = \sqrt{(-3 - (-5))^2 + (0 - (-3))^2}$

(C) $VU = d = \sqrt{(5 - (2))^2 + (2 - 4)^2}$

(D) $VW = d = \sqrt{(0 - (5))^2 + (1 - 2)^2}$

(E) $JH = \sqrt{13}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Distance Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Apply distance formula to JH

Apply distance formula to VU

Identify matching options

Answer: