Math / Geometry

Question2. The following triangles are congruent. Use this to answer the questions below: a. What is the measure of angle JLK? b. What is the measure of angle GIH? $\qquad$ c. What is the length of line segment HI? $\qquad$ d. Write the congruence statement for these triangles $\qquad$

Studdy Solution

STEP 1

1. Triangles JLK and GIH are congruent.
2. Congruent triangles have corresponding angles and sides that are equal.
3. The sum of the angles in a triangle is $180^\circ$ .

STEP 2

1. Determine the measure of angle JLK.
2. Determine the measure of angle GIH.
3. Determine the length of line segment HI.
4. Write the congruence statement for the triangles.

STEP 3

Determine the measure of angle JLK:
- Given angles in triangle JLK are $46^\circ$ and $101^\circ$ . - Use the angle sum property of triangles:
$\text{Measure of angle JLK} = 180^\circ - 46^\circ - 101^\circ$
Calculate:
$= 33^\circ$

STEP 4

Determine the measure of angle GIH:
- Given angle in triangle GIH is $33^\circ$ . - Since triangles are congruent, corresponding angles are equal. - Therefore, the measure of angle GIH is $101^\circ$ .

STEP 5

Determine the length of line segment HI:
- Given sides in triangle JLK are $7$ and $9$ . - Given sides in triangle GIH are $6$ and $7$ . - Since triangles are congruent, corresponding sides are equal. - Therefore, the length of line segment HI is $9$ .

STEP 6

Write the congruence statement for the triangles:
- Corresponding vertices must be matched. - Triangle JLK is congruent to triangle GIH, so:
$\triangle JLK \cong \triangle GIH$
The measures and congruence statement are: a. Measure of angle JLK: $33^\circ$ b. Measure of angle GIH: $101^\circ$ c. Length of line segment HI: $9$ d. Congruence statement: $\triangle JLK \cong \triangle GIH$

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Question2. The following triangles are congruent. Use this to answer the questions below: a. What is the measure of angle JLK? b. What is the measure of angle GIH? $\qquad$ c. What is the length of line segment HI? $\qquad$ d. Write the congruence statement for these triangles $\qquad$

Studdy Solution

STEP 1

1. Triangles JLK and GIH are congruent.
2. Congruent triangles have corresponding angles and sides that are equal.
3. The sum of the angles in a triangle is $180^\circ$ .

STEP 2

1. Determine the measure of angle JLK.
2. Determine the measure of angle GIH.
3. Determine the length of line segment HI.
4. Write the congruence statement for the triangles.

STEP 3

Determine the measure of angle JLK:
- Given angles in triangle JLK are $46^\circ$ and $101^\circ$ . - Use the angle sum property of triangles:
$\text{Measure of angle JLK} = 180^\circ - 46^\circ - 101^\circ$
Calculate:
$= 33^\circ$

STEP 4

Determine the measure of angle GIH:
- Given angle in triangle GIH is $33^\circ$ . - Since triangles are congruent, corresponding angles are equal. - Therefore, the measure of angle GIH is $101^\circ$ .

STEP 5

Determine the length of line segment HI:
- Given sides in triangle JLK are $7$ and $9$ . - Given sides in triangle GIH are $6$ and $7$ . - Since triangles are congruent, corresponding sides are equal. - Therefore, the length of line segment HI is $9$ .

STEP 6

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Question2. The following triangles are congruent. Use this to answer the questions below: a. What is the measure of angle JLK? b. What is the measure of angle GIH? \qquad c. What is the length of line segment HI? \qquad d. Write the congruence statement for these triangles \qquad

Studdy Solution

STEP 1

1. Triangles JLK and GIH are congruent.2. Congruent triangles have corresponding angles and sides that are equal.3. The sum of the angles in a triangle is 180∘180^\circ180∘.

STEP 2

1. Determine the measure of angle JLK.2. Determine the measure of angle GIH.3. Determine the length of line segment HI.4. Write the congruence statement for the triangles.

STEP 3

STEP 4

Determine the measure of angle GIH:- Given angle in triangle GIH is 33∘33^\circ33∘. - Since triangles are congruent, corresponding angles are equal. - Therefore, the measure of angle GIH is 101∘101^\circ101∘.

STEP 5

Determine the length of line segment HI:- Given sides in triangle JLK are 777 and 999. - Given sides in triangle GIH are 666 and 777. - Since triangles are congruent, corresponding sides are equal. - Therefore, the length of line segment HI is 999.

STEP 6

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Question2. The following triangles are congruent. Use this to answer the questions below: a. What is the measure of angle JLK? b. What is the measure of angle GIH? $\qquad$ c. What is the length of line segment HI? $\qquad$ d. Write the congruence statement for these triangles $\qquad$

1. Triangles JLK and GIH are congruent.
2. Congruent triangles have corresponding angles and sides that are equal.
3. The sum of the angles in a triangle is $180^\circ$ .

1. Determine the measure of angle JLK.
2. Determine the measure of angle GIH.
3. Determine the length of line segment HI.
4. Write the congruence statement for the triangles.

Determine the measure of angle GIH:
- Given angle in triangle GIH is $33^\circ$ . - Since triangles are congruent, corresponding angles are equal. - Therefore, the measure of angle GIH is $101^\circ$ .

Determine the length of line segment HI:
- Given sides in triangle JLK are $7$ and $9$ . - Given sides in triangle GIH are $6$ and $7$ . - Since triangles are congruent, corresponding sides are equal. - Therefore, the length of line segment HI is $9$ .