Question
Parallelogram is shown with vertices at negative 5 comma 1, negative 4 comma 3, negative 1 comma 3, and negative 2 comma 1.
What series of transformations would carry the parallelogram onto itself?
(x + 0, y − 6), 180° rotation, (x − 2, y − 2)
(x + 0, y − 6), 90° clockwise rotation, (x − 2, y − 2)
(x + 6, y + 0), 180° rotation, (x + 0, y + 4)
(x + 6, y + 0), 90° clockwise rotation, (x + 0, y + 4)
Question 2
(Multiple Choice Worth 1 Points)
(02.06 LC)
The figure below shows a quadrilateral ABCD. Sides AB and DC are congruent and parallel:
A quadrilateral ABCD is shown with the opposite sides AB and DC shown parallel and equal.
A student wrote the following sentences to prove that quadrilateral ABCD is a parallelogram:
Side AB is parallel to side DC, so the alternate interior angles, angle ABD and angle CDB, are congruent. Side AB is equal to side DC, and DB is the side common to triangles ABD and CDB. Therefore, the triangles ABD and CDB are congruent by ________. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB form a pair of alternate interior angles. Therefore, AD is congruent and parallel to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Which phrase best completes the student's proof?
AAS Postulate
HL Postulate
SAS Postulate
SSS Postulate
Question 3
(Multiple Choice Worth 1 Points)
(02.03 MC)
triangle ADB, point C lies on segment AB and forms segment CD, segment AC is congruent to segment BC. Point A is labeled jungle gym and point B is labeled monkey bars.
Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
If segment AD ≅ segment CD, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
If segment AD ≅ segment CD, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If m∠ACD = 90° then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
If m∠ACD = 90° then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
Question 4
(Multiple Choice Worth 1 Points)
(02.05 MC)
In triangle ABC shown below, side AB is 10 and side AC is 8:
Triangle ABC with segment joining point D on segment AB and point E on segment AC.
Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Segment AD is 5, and segment AE is 4.
Segment AD is 4, and segment AE is 8.
Segment AD is 4, and segment AE is 5.
Segment AD is 5, and segment AE is 2.
Question 5
(Multiple Choice Worth 1 Points)
(02.01 MC)
Rectangle J′K′L′M′ shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.
Rectangle JKLM is drawn on the grid with vertices J at negative 7, negative 6. K is at negative 4, negative 6. L is at negative 4, negative 2. M is at negative 7, negative 2. Rectangle J prime K prime L prime M prime is drawn with vertices J at prime 6, negative 9. K prime is at 9, negative 9. L prime 9, negative 5. M prime is at 6, negative 5. Trapezoid STUV is drawn with vertices at S 3, 2. T is at 5, 5. U is at 2, 6. V is at 1, 4.
What will be the location of T′ in the image trapezoid S′T′U′V′?
(18, −2)
(18, 2)
(15, −2)
(15, 2)
Question 6
(Multiple Choice Worth 1 Points)
(02.03 LC)
If triangle ABC is congruent to triangle DEF, which statement is not true?
segment AB ≅ segment DE
∠C ≅ ∠E
segment BC ≅ segment EF
∠A ≅ ∠D
Question 7
(Multiple Choice Worth 1 Points)
(02.04, 02.05 LC)
Triangle ABC is a right triangle. Point D is the midpoint of side AB, and point E is the midpoint of side AC. The measure of ∠ADE is 47°.
Triangle ABC with segment DE. Angle ADE measures 47 degrees.
The proof, with a missing reason, proves that the measure of ∠ECB is 43°.
Statement Reason
m∠ADE = 47° Given
m∠DAE = 90° Definition of a right angle
m∠AED = 43° ?
segment DE joins the midpoints of segment AB and segment AC Given
segment DE is parallel to segment BC Midsegment of a Triangle Theorem
∠ECB ≅ ∠AED Corresponding angles are congruent
m∠ECB = 43° Substitution property
Which theorem can be used to fill in the missing reason?
Concurrency of Medians Theorem
Isosceles Triangle Theorem
Triangle Inequality Theorem
Triangle Sum Theorem
Question 8
(Multiple Choice Worth 1 Points)
(02.06 MC)
quadrilateral PQRS with diagonals PR and SQ that intersect at point T
If quadrilateral PQRS is a rectangle, then which of the following is true?
∠PSQ ≅ ∠QSR
segment SR ≅ segment RQ
∠STP ≅ ∠QTR
segment PS ≅ segment PR
Question 9
(Multiple Choice Worth 1 Points)
(02.04 MC)
In triangle DEF, if m∠D = (4x)°, m∠E = (2x − 3)°, and m∠F = (x + 8)°, what is the value of x?
51
29
26
25
Question 10
(Multiple Choice Worth 1 Points)
(02.02 LC)
Rectangle ABCD is shown. A is at negative 5, 1. B is at negative 5, 3. C is at negative 1, 3. D is at negative 1, 1.
Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?
(x, y) → (−x, −y); A′ is at (5, −1)
(x, y) → (−y, x); A′ is at (−1, −5)
(x, y) → (y, −x); A′ is at (1, 5)
(x, y) → (x, −y); A′ is at (−5, −1)
Question 11
(Multiple Choice Worth 1 Points)
(02.03 MC)
polygon ABCDE is on a coordinate plane with point A at 2, 4 and point B at 4, 3 and point C at 3, 2 and point D at 1, 2 and point E at 0, 3
Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A′ is at (−2, 4) and the image of D′ is at (−1, 2). Which transformation can be used to show that ABCDE and its image are congruent?
Rotate ABCDE 90° counterclockwise.
Translate ABCDE left 4 units and down 2 units.
Reflect ABCDE over the y-axis.
Rotate ABCDE 90° clockwise.
Question 12
(Multiple Choice Worth 1 Points)
(02.06 MC)
The figure below shows rectangle ABCD with diagonals segment AC and segment BD:
A rectangle ABCD is shown with diagonals AC and BD.
Zinnia wrote the following proof to show that the diagonals of rectangle ABCD are congruent:
Zinnia's proof:
Statement 1: Rectangle ABCD is given
Statement 2: segment AD ≅ segment BC because opposite sides of a rectangle are congruent
Statement 3: segment DC ≅ segment DC by the reflexive property of congruence
Statement 4: Angles ADC and BCD are both right angles by definition of a rectangle
Statement 5: Angles ADC and BCD are congruent because all right angles are congruent
Statement 6:
Statement 7: segment AC ≅ segment BD by CPCTC
Which statement below completes Zinnia's proof?
Triangles ADC and BCD are congruent (by ASA postulate)
Triangles ADC and BCD are congruent (by SAS postulate)
Triangles ADC and CBA are congruent (by ASA postulate)
Triangles ADC and CBA are congruent (by SAS postulate)
Question 13
(Multiple Choice Worth 1 Points)
(02.01 MC)
figure H has four sides with vertices at 1, 2 and 2, 3 and 3, 2 and 2, 1
Which series of transformations will not map figure H onto itself?
(x + 0, y − 2), reflection over y = 1
(x + 2, y − 0), reflection over x = 3
(x + 3, y + 3), reflection over y = −x + 7
(x − 3, y − 3), reflection over y = −x + 2
Question 14
(Multiple Choice Worth 1 Points)
(02.04 MC)
Triangles ABD and CBD are shown.
Triangle A C D is divided into two smaller triangles which are triangle A B D and D B C which share a common side B D. Point B lies on segment A C. Segment A B is congruent to segment B C.
If m∠ABD = 100°, what is the relationship between AD and CD?
AD + DC < AC
CD = AD
CD > AD
CD < AD
Question 15
(Multiple Choice Worth 1 Points)
(02.03 MC)
triangles FEG and NOM
Ebony is cutting dough for pastries in her bakery. She needs all the pieces to be congruent triangles and has ensured that segment EF ≅ segment ON and ∠MON ≅ ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by SAS?
segment OM and segment EF
segment EG and segment OM
segment NM and segment FG
segment EG and segment MN
Answers
Answered by
GPT-4o mini
Here's the solution to each question based on the information provided:
### Question 1
For the parallelogram with vertices at specified coordinates, a series of transformations that will carry the parallelogram onto itself involves transformations that don't change its overall shape or orientation.
**Answer:** (x + 0, y − 6), 180° rotation, (x − 2, y − 2)
### Question 2
To prove that quadrilateral ABCD is a parallelogram by using congruence of trianglesABD and CDB, the key is the criterion used for triangle congruence.
**Answer:** SAS Postulate
### Question 3
To show that point D is equidistant from points A (jungle gym) and B (monkey bars), use the property of the perpendicular bisector.
**Answer:** If m∠ACD = 90° then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
### Question 4
To prove that segment DE is parallel to segment BC and half its length, you need the segment lengths to maintain the ratio of the sides.
**Answer:** Segment AD is 5, and segment AE is 4.
### Question 5
To determine the location of T' after applying the same transformation applied to rectangle JKLM onto trapezoid STUV, you look at the transformation rules and find the new coordinates.
**Answer:** (18, 2)
### Question 6
If triangle ABC is congruent to triangle DEF, every side and angle corresponds accordingly. The incorrect statement would be the one that contradicts this.
**Answer:** segment BC ≅ segment EF
### Question 7
To prove angle ECB is 43° given the properties of the triangle and the midpoints, you need a theorem that relates the angles and midpoints.
**Answer:** Triangle Sum Theorem
### Question 8
In a rectangle, opposite angles are congruent, and adjacent angles are supplementary.
**Answer:** ∠STP ≅ ∠QTR
### Question 9
Set up the equation from the angles of triangle DEF knowing that the sum of angles in a triangle equals 180° to solve for x.
**Answer:** 29
### Question 10
For a 180° rotation, the coordinates of point A will change according to the rule given.
**Answer:** (x, y) → (−x, −y); A′ is at (5, −1)
### Question 11
The transformation can be identified based on the new positions of points A' and D'.
**Answer:** Reflect ABCDE over the y-axis.
### Question 12
To complete the proof showing that the diagonals are congruent, the common postulate of triangle congruence needs to be stated correctly.
**Answer:** Triangles ADC and BCD are congruent (by SAS postulate)
### Question 13
To find which series of transformations will not map the figure onto itself, look for inconsistencies.
**Answer:** (x + 2, y − 0), reflection over x = 3
### Question 14
In triangle relationships, the sum of two sides must be greater than the third side.
**Answer:** AD + DC < AC
### Question 15
To establish the congruence of triangles FEG and NOM by the SAS criterion, you must compare the remaining sides given that one side and the included angle are already known.
**Answer:** segment EG and segment OM
Feel free to ask if you need further explanations on any of these!
### Question 1
For the parallelogram with vertices at specified coordinates, a series of transformations that will carry the parallelogram onto itself involves transformations that don't change its overall shape or orientation.
**Answer:** (x + 0, y − 6), 180° rotation, (x − 2, y − 2)
### Question 2
To prove that quadrilateral ABCD is a parallelogram by using congruence of trianglesABD and CDB, the key is the criterion used for triangle congruence.
**Answer:** SAS Postulate
### Question 3
To show that point D is equidistant from points A (jungle gym) and B (monkey bars), use the property of the perpendicular bisector.
**Answer:** If m∠ACD = 90° then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
### Question 4
To prove that segment DE is parallel to segment BC and half its length, you need the segment lengths to maintain the ratio of the sides.
**Answer:** Segment AD is 5, and segment AE is 4.
### Question 5
To determine the location of T' after applying the same transformation applied to rectangle JKLM onto trapezoid STUV, you look at the transformation rules and find the new coordinates.
**Answer:** (18, 2)
### Question 6
If triangle ABC is congruent to triangle DEF, every side and angle corresponds accordingly. The incorrect statement would be the one that contradicts this.
**Answer:** segment BC ≅ segment EF
### Question 7
To prove angle ECB is 43° given the properties of the triangle and the midpoints, you need a theorem that relates the angles and midpoints.
**Answer:** Triangle Sum Theorem
### Question 8
In a rectangle, opposite angles are congruent, and adjacent angles are supplementary.
**Answer:** ∠STP ≅ ∠QTR
### Question 9
Set up the equation from the angles of triangle DEF knowing that the sum of angles in a triangle equals 180° to solve for x.
**Answer:** 29
### Question 10
For a 180° rotation, the coordinates of point A will change according to the rule given.
**Answer:** (x, y) → (−x, −y); A′ is at (5, −1)
### Question 11
The transformation can be identified based on the new positions of points A' and D'.
**Answer:** Reflect ABCDE over the y-axis.
### Question 12
To complete the proof showing that the diagonals are congruent, the common postulate of triangle congruence needs to be stated correctly.
**Answer:** Triangles ADC and BCD are congruent (by SAS postulate)
### Question 13
To find which series of transformations will not map the figure onto itself, look for inconsistencies.
**Answer:** (x + 2, y − 0), reflection over x = 3
### Question 14
In triangle relationships, the sum of two sides must be greater than the third side.
**Answer:** AD + DC < AC
### Question 15
To establish the congruence of triangles FEG and NOM by the SAS criterion, you must compare the remaining sides given that one side and the included angle are already known.
**Answer:** segment EG and segment OM
Feel free to ask if you need further explanations on any of these!