Answers Geometry Concepts and ConnectionsCongruence

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Which rigid transformation would map triangle ABC to triangle ABF ?

a rotation about point cap A

a reflection across the line containing line segment CB

a rotation about point cap b

a reflection across the line containing line segment BA

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Which best explains whether or not triangles RST and ACB are congruent?

The figures are congruent. triangle RST can be mapped to triangle ACB by a reflection over the x -axis and a translation 2 units to the left.

The figures are not congruent. Point cap r corresponds to point cap A , but cap s corresponds to cap b and cap t corresponds to cap c .

The figures are not congruent. Point cap r does not correspond with point cap A .

The figures are congruent. triangle RST can be mapped to triangle ACB by a reflection over the y -axis and a translation 2 units down.

Quinton tried to transform triangle FGH according to the rule open paren x comma y close paren rightarrow open paren negative y comma x close paren Which best describes his attempt?

Incorrect. He transformed the triangle according to the rule open paren x comma y close paren rightarrow open paren negative x comma negative y close paren .

Incorrect. He transformed the triangle according to the rule open paren x comma y close paren rightarrow open paren negative y comma negative x close paren .

Correct. He transformed the triangle according to the rule open paren x comma y close paren rightarrow open paren negative y comma x close paren .

Incorrect. He transformed the triangle according to the rule open paren x comma y close paren rightarrow open paren y comma negative x close paren .

Triangle RST is rotated 180 degrees about the origin, and then translated up 3 units. Which congruency statement describes the figures?

triangle RST is congruent to triangle ABC

triangle RST is congruent to triangle ACB

triangle RST is congruent to triangle BCA

triangle RST is congruent to triangle BAC

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

angle cap h cap f cap g is congruent to angle cap k cap j cap g because alternate interior angles are congruent.

angle cap f cap h cap g is congruent to angle cap j cap k cap g because right angles are congruent.

angle cap f cap g cap h is congruent to angle cap k cap g cap j because vertical angles are congruent.

angle cap j cap k cap g is congruent to angle cap h cap f cap g because vertical angles are congruent.

A point has the coordinates (m, 0) and m≠0. Which reflection of the point will produce an image located at open paren 0 comma negative m close paren ?

a reflection of the point across the x -axis

a reflection of the point across the line y is equal to x

a reflection of the point across the line y is equal to negative x

a reflection of the point across the y -axis

A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes the translation?

cap t sub negative 9 comma negative 1 times open paren x comma y close paren

cap t sub negative 1 comma negative 9 times open paren x comma y close paren

cap t sub 1 comma negative 9 times open paren x comma y close paren

cap t sub negative 9 comma 1 times open paren x comma y close paren

Triangle EFG has vertices E(−3, 4), F(−5,−1), and G(1, 1). The triangle is translated so that the coordinates of the image are E′⁡(−1, 0), F′⁡(−3,−5), and G′⁡(3,−3). Which rule was used to translate the image?

cap t sub 2 comma negative 4 times open paren x comma y close paren

cap t sub negative 2 comma negative 4 times open paren x comma y close paren

cap t sub negative 4 comma negative 4 times open paren x comma y close paren

cap t sub 4 comma negative 4 times open paren x comma y close paren

Which pair of triangles can be proven congruent by the HL theorem?

Image with description Two separate right triangles are shown. Each triangle has a right-angle marker, and the side opposite the right angle has a single tick mark. No other sides are marked.

Image with description Two separate right triangles are shown. In each triangle, the side opposite the right angle has double tick marks, and one side adjacent to the right angle has a single tick mark.

Image with description Two separate triangles are shown. In the left triangle, one side has a single tick mark, the opposite side has double tick marks, and the angle between the single-tick side and an unmarked side has an arc mark. In the right triangle, one side has a single tick mark, the opposite side has double tick marks, and the angle between the single-tick side and an unmarked side has an arc mark. No right-angle markers are shown.

Image with description Two separate triangles are shown with no right-angle markers. In the upper triangle, the left side has a single tick mark, the lower-right side has double tick marks, and the upper-right side has triple tick marks. In the lower triangle, the bottom side has a single tick mark, the right slanted side has double tick marks, and the left side has triple tick marks.

First, translate ____________________. Next, rotate triangle ABC about cap b to align the sides and angles.

vertex cap A to vertex cap z

vertex cap b to vertex cap z

vertex cap A to vertex cap y

vertex cap b to vertex cap y

What is the rule for the reflection?

r sub x - axis times open paren x comma y close paren rightarrow open paren x comma negative y close paren

r sub y - axis times open paren x comma y close paren rightarrow open paren negative x comma y close paren

r sub y - axis times open paren x comma y close paren rightarrow open paren x comma negative y close paren

r sub x - axis times open paren x comma y close paren rightarrow open paren negative x comma y close paren

Which rule describes the transformation?

cap r sub 0 comma 180 degrees

cap r sub 0 comma 270 degrees

cap r sub 0 comma 90 degrees

cap r sub 0 comma 360 degrees

Which composition of transformations maps figure RSTUV to figure cap r double prime cap s double prime cap t double prime cap u double prime cap v double prime ?

a reflection across line n followed by a 270 degrees rotation about point cap p

a reflection across line n followed by a translation down and to the right

a translation down followed by a 270 degrees rotation about point cap p

a translation down followed by a reflection across line n

The first transformation for this composition is [________], and the second transformation is a translation down and to the right.

a 270 degrees clockwise rotation about point cap p

a 90 degrees clockwise rotation about point cap p

a 90 degrees clockwise rotation about point cap l

a 270 degrees clockwise rotation about point cap l

Could triangle ABC be congruent to triangle ADC by SSS? Explain.

No, because line segment AB is not congruent to line segment AC .

Yes, but only if line segment BC is congruent to line segment DC .

Yes, but only if line segment AB is congruent to line segment DC .

No, because line segment AB is congruent to line segment DA .

Nessa proved that these triangles are congruent using ASA. Roberto proved that they are congruent using AAS. Which statement and reason would be included in Roberto’s proof that was not included in Nessa’s proof? Given: angle cap b is congruent to angle cap n ; line segment cap b cap c is congruent to line segment cap n cap m ; angle cap c is right; angle cap m is right Prove: triangle cap A cap b cap c is congruent to triangle cap q cap n cap m

angle cap c is congruent to angle cap m because right angles are congruent.

line segment cap b cap c is congruent to line segment cap n cap m because it is given.

angle cap A is congruent to angle cap q because of the third angle theorem.

line segment cap A cap b is congruent to line segment cap q cap n because they are both opposite a right angle.

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