Copy of Geo Unit 2 - Lesson 6 Page 230-232 (11/4/2024)

Last updated over 1 year ago

6 questions

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Library

Copy of Geo Unit 2 - Lesson 6 Page 230-232 (11/4/2024)

Last updated over 1 year ago

6 questions

1

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Tyler has written an incorrect proof to show that quadrilateral ABCD is a parallelogram. He knows segments AB and DC are congruent. He also knows angles ABC and ADC are congruent. Find the mistake in his proof.

Segment AC is congruent to itself, so triangle ABC is congruent to triangle ADC by Side-Angle-Side Triangle Congruence Theorem.  Since the triangles are congruent, so are the corresponding parts, and so angle DAC is congruent to ACB.  In quadrilateral ABCD, AB is congruent to CD and AD is parallel to CB. Since AD is parallel to CB, alternate interior angles DAC and BCA are congruent. Since alternate interior angles are congruent, AB must be parallel to CD. Quadrilateral ABCD must be a parallelogram since both pairs of opposite sides are parallel.
Tyler does not have the congruent parts to use the Side Angle-Side Triangle Congruence Theorem. He has two pairs of sides and a pair of angles, but the _______  are not included between the _______ .

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Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of angle ABD.

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Draggable item		Corresponding Item

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Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle is isosceles? Select all that apply.

Angle BAD is congruent to angle ABC.

Line AB is an angle bisector of DAC.

Angle BDC is congruent to angle BCD.

Triangle DAB is congruent to triangle CAB.

Angle ABD is congruent to angle ABC.

Tyler has written an incorrect proof to show that quadrilateral ABCD is a parallelogram. He knows segments AB and DC are congruent. He also knows angles ABC and ADC are congruent. Find the mistake in his proof.

Segment AC is congruent to itself, so triangle ABC is congruent to triangle ADC by Side-Angle-Side Triangle Congruence Theorem.  Since the triangles are congruent, so are the corresponding parts, and so angle DAC is congruent to ACB.  In quadrilateral ABCD, AB is congruent to CD and AD is parallel to CB. Since AD is parallel to CB, alternate interior angles DAC and BCA are congruent. Since alternate interior angles are congruent, AB must be parallel to CD. Quadrilateral ABCD must be a parallelogram since both pairs of opposite sides are parallel.
Tyler does not have the congruent parts to use the Side Angle-Side Triangle Congruence Theorem. He has two pairs of sides and a pair of angles, but the _______  are not included between the _______ .

Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of angle ABD.

Here are some statements about 2 zigzags. Put them in order to prove figure ABC is congruent to figure DEF.
1: Therefore, figure ABC is congruent to figure DEF.
2: If necessary, rotate the image of figure ABC around point D to be sure the image of C, which we will call C', will coincide with point  F.
3: Segments AB and DE are the same length so they are congruent. Therefore, there is a rigid motion that takes AB to DE. Determine which rigid motion to use.
4: Since points C' and F are the same distance along the same ray from E they have to be in the same place. Therefore Point B must now coincide with Point E.
5: Translate figure ABC along the directed line segment AD. 
(enter the number of each step in the correct order)
First step: _______ 
Second step: _______ 
Third step: _______ 
Fourth step: _______ 
Last step: _______ 

Match each statement using only the information shown in the pairs of congruent triangles.

Draggable item		Corresponding Item
In the 2 triangles there are 3 pairs of congruent sides.
The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.
The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

Triangle ABC is congruent to triangle EDF. So, Priya knows that there is a sequence of rigid motions that takes ABC to EDF.
Select all true statements after the transformations:

Segment AB coincides with segment EF.

Segment BC coincides with segment DF.

Segment AC coincides with segment ED.

Angle A coincides with angle E.

Angle C coincides with angle E.

Angle C coincides with angle F.

Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle  is isosceles? Select all that apply.

Angle BAD is congruent to angle ABC.

Line AB is an angle bisector of DAC.

Angle BDC is congruent to angle BCD.

Triangle DAB is congruent to triangle CAB.

Angle ABD is congruent to angle ABC.

Here are some statements about 2 zigzags. Put them in order to prove figure ABC is congruent to figure DEF.
1: Therefore, figure ABC is congruent to figure DEF.
2: If necessary, rotate the image of figure ABC around point D to be sure the image of C, which we will call C', will coincide with point  F.
3: Segments AB and DE are the same length so they are congruent. Therefore, there is a rigid motion that takes AB to DE. Determine which rigid motion to use.
4: Since points C' and F are the same distance along the same ray from E they have to be in the same place. Therefore Point B must now coincide with Point E.
5: Translate figure ABC along the directed line segment AD. 
(enter the number of each step in the correct order)
First step: _______ 
Second step: _______ 
Third step: _______ 
Fourth step: _______ 
Last step: _______ 

Match each statement using only the information shown in the pairs of congruent triangles.

In the 2 triangles there are 3 pairs of congruent sides.

The 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of another triangle.

The 2 angles and the included side of one triangle are congruent to 2 angles and the included side of another triangle.

Triangle ABC is congruent to triangle EDF. So, Priya knows that there is a sequence of rigid motions that takes ABC to EDF.
Select all true statements after the transformations:

Segment AB coincides with segment EF.

Segment BC coincides with segment DF.

Segment AC coincides with segment ED.

Angle A coincides with angle E.

Angle C coincides with angle E.

Angle C coincides with angle F.

Copy of Geo Unit 2 - Lesson 6 Page 230-232 (11/4/2024)

Copy of Geo Unit 2 - Lesson 6 Page 230-232 (11/4/2024)

Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of angle ABD.

Triangle DAC is isosceles with congruent sides AD and AC. Which additional given information is sufficient for showing that triangle is isosceles? Select all that apply.

Triangles ACD and BCD are isosceles. Angle BAC has a measure of 18 degrees and angle BDC has a measure of 48 degrees. Find the measure of angle ABD.

Match each statement using only the information shown in the pairs of congruent triangles.

Triangle ABC is congruent to triangle EDF. So, Priya knows that there is a sequence of rigid motions that takes ABC to EDF.Select all true statements after the transformations:

Triangle ABC is congruent to triangle EDF. So, Priya knows that there is a sequence of rigid motions that takes ABC to EDF.
Select all true statements after the transformations: