QuestionTranslate triangle $\triangle FGH$ down 2 units and left 5 units to get triangle $KLM$ . Complete the congruence statements:
$\begin{aligned} \overline{GH} \cong & \\ \angle K \cong & \\ \overline{MK} \cong & \\ H \cong & \\ \end{aligned}$

Studdy Solution

STEP 1

Assumptions1. Triangle $\triangle FGH$ is translated units down and5 units to the left to form a new triangle $\triangle KLM$ . . The translation does not change the shape or size of the triangle, it only changes its position.

STEP 2

The translation of a figure does not change its size or shape, it only changes its position. Therefore, the lengths of corresponding sides and the measures of corresponding angles remain the same before and after the translation.

STEP 3

The line segment $\overline{GH}$ in $\triangle FGH$ corresponds to $\overline{LM}$ in $\triangle KLM$ after the translation. Therefore, we can say that $\overline{GH} \cong \overline{LM}$ .

STEP 4

The angle $K$ in $\triangle KLM$ corresponds to angle $$ in $\triangle FGH$ before the translation. Therefore, we can say that $\angle K \cong \angle F$.

STEP 5

The line segment $\overline{MK}$ in $\triangle KLM$ corresponds to $\overline{HF}$ in $\triangle FGH$ before the translation. Therefore, we can say that $\overline{MK} \cong \overline{HF}$ .

STEP 6

The vertex $H$ in $\triangle FGH$ corresponds to vertex $M$ in $\triangle KLM$ after the translation. Therefore, we can say that $H \cong M$ .
So, the completed congruence statements are $\begin{aligned} \overline{GH} \cong & \overline{LM} \\ \angle K \cong & \angle F \\ \overline{MK} \cong & \overline{HF} \\ H \cong & M \\ \end{aligned}$

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QuestionTranslate triangle $\triangle FGH$ down 2 units and left 5 units to get triangle $KLM$ . Complete the congruence statements:
$\begin{aligned} \overline{GH} \cong & \\ \angle K \cong & \\ \overline{MK} \cong & \\ H \cong & \\ \end{aligned}$

Studdy Solution

STEP 1

Assumptions1. Triangle $\triangle FGH$ is translated units down and5 units to the left to form a new triangle $\triangle KLM$ . . The translation does not change the shape or size of the triangle, it only changes its position.

STEP 2

The translation of a figure does not change its size or shape, it only changes its position. Therefore, the lengths of corresponding sides and the measures of corresponding angles remain the same before and after the translation.

STEP 3

The line segment $\overline{GH}$ in $\triangle FGH$ corresponds to $\overline{LM}$ in $\triangle KLM$ after the translation. Therefore, we can say that $\overline{GH} \cong \overline{LM}$ .

STEP 4

The angle $K$ in $\triangle KLM$ corresponds to angle $$ in $\triangle FGH$ before the translation. Therefore, we can say that $\angle K \cong \angle F$.

STEP 5

The line segment $\overline{MK}$ in $\triangle KLM$ corresponds to $\overline{HF}$ in $\triangle FGH$ before the translation. Therefore, we can say that $\overline{MK} \cong \overline{HF}$ .

STEP 6

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Studdy Solution

STEP 1

Assumptions1. Triangle △FGH\triangle FGH△FGH is translated units down and5 units to the left to form a new triangle △KLM\triangle KLM△KLM. . The translation does not change the shape or size of the triangle, it only changes its position.

STEP 2

The translation of a figure does not change its size or shape, it only changes its position. Therefore, the lengths of corresponding sides and the measures of corresponding angles remain the same before and after the translation.

STEP 3

The line segment GH‾\overline{GH}GH in △FGH\triangle FGH△FGH corresponds to LM‾\overline{LM}LM in △KLM\triangle KLM△KLM after the translation. Therefore, we can say that GH‾≅LM‾\overline{GH} \cong \overline{LM}GH≅LM.

STEP 4

The angle KKK in △KLM\triangle KLM△KLM corresponds to angle $$ in $\triangle FGH$ before the translation. Therefore, we can say that $\angle K \cong \angle F$.

STEP 5

The line segment MK‾\overline{MK}MK in △KLM\triangle KLM△KLM corresponds to HF‾\overline{HF}HF in △FGH\triangle FGH△FGH before the translation. Therefore, we can say that MK‾≅HF‾\overline{MK} \cong \overline{HF}MK≅HF.

STEP 6

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Assumptions1. Triangle $\triangle FGH$ is translated units down and5 units to the left to form a new triangle $\triangle KLM$ . . The translation does not change the shape or size of the triangle, it only changes its position.

The line segment $\overline{GH}$ in $\triangle FGH$ corresponds to $\overline{LM}$ in $\triangle KLM$ after the translation. Therefore, we can say that $\overline{GH} \cong \overline{LM}$ .

The angle $K$ in $\triangle KLM$ corresponds to angle $$ in $\triangle FGH$ before the translation. Therefore, we can say that $\angle K \cong \angle F$.

The line segment $\overline{MK}$ in $\triangle KLM$ corresponds to $\overline{HF}$ in $\triangle FGH$ before the translation. Therefore, we can say that $\overline{MK} \cong \overline{HF}$ .