Math  /  Geometry

QuestionNarese \qquad Oate
8. 10ABD Module Assessment 1

1 Thangle Efis strown on the coordinate grid. The quadrilateral is rellectel across the yy-axis to crate triangle EfG: Q.10480. 2
Which statement is true? A Triangle E'F G' is congruent to triangle EFG. 8 The area of triangle E'FG is greater than the area of triangle EFG. C The permeter of triangle EFGE^{\prime} F^{\prime} G^{\prime} is less than the perimeter of triangle EFG. D The angle measures of triangle E'F'G' are not congruent to the angle measures of triangle EFG.

Studdy Solution

STEP 1

1. Triangle EFG is drawn on a coordinate grid.
2. The triangle is reflected across the y y -axis to create triangle EFG E'F'G' .
3. Reflections preserve congruence and do not alter the size or shape of geometric figures.

STEP 2

1. Understand the properties of reflections.
2. Analyze the congruence of triangles.
3. Evaluate the area of the triangles.
4. Compare the perimeters of the triangles.
5. Assess the angle measures of the triangles.

STEP 3

Understand the properties of reflections: - A reflection across the y y -axis changes the sign of the x x -coordinates of the points but preserves the y y -coordinates. - Reflections preserve the size and shape of geometric figures, meaning the reflected figure is congruent to the original.

STEP 4

Analyze the congruence of triangles: - Since reflections preserve congruence, triangle EFG E'F'G' is congruent to triangle EFG EFG .

STEP 5

Evaluate the area of the triangles: - The area of a triangle is preserved under reflection. Therefore, the area of triangle EFG E'F'G' is equal to the area of triangle EFG EFG .

STEP 6

Compare the perimeters of the triangles: - The perimeter of a triangle is also preserved under reflection. Therefore, the perimeter of triangle EFG E'F'G' is equal to the perimeter of triangle EFG EFG .

STEP 7

Assess the angle measures of the triangles: - Reflections preserve angle measures. Therefore, the angle measures of triangle EFG E'F'G' are congruent to the angle measures of triangle EFG EFG .
The true statement is: A: Triangle EFG is congruent to triangle EFG. \text{A: Triangle } E'F'G' \text{ is congruent to triangle } EFG.

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