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 2(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 3(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?
figure L has four sides with vertices at 0, 1 and 3, 4 and 5, 2 and 2, negative 1
Which series of transformations will not map figure L onto itself?
(x + 1, y − 4), reflection over y = x − 4
(x − 4, y − 4), reflection over y = −x
(x + 3, y − 3), reflection over y = x − 4
(x + 4, y + 4), reflection over y = −x + 8
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 8, negative 8, K at negative 4, negative 8, L at negative 4, negative 5, and M at negative 8, negative 5. Rectangle J prime K prime L prime M prime is drawn with vertices J prime at 2, negative 5, K prime 6, negative 5, L prime 6, negative 2, and M prime 2, negative 2. Trapezoid STUV is drawn with vertices S at 1, 4. T is at 6, 4. U is at 4, 6. V is at 2, 6.
What will be the location of T′ in the image trapezoid S′T′U′V′?
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 is congruent to ∠GEF. What would Ebony need to compare in order to make sure the triangles are congruent by AAS?
segment EG and segment OM
∠EFG and ∠ONM
segment NM and segment FG
∠EGF and ∠OMN
Question 7(Multiple Choice Worth 1 points)
(02.06 MC)
The figure below shows rectangle ABCD with diagonals segment AC and segment DB:
A rectangle ABCD is shown with diagonals AC and BD.
Jimmy wrote the following proof to show that the diagonals of rectangle ABCD are congruent:
Jimmy's proof:
Statement 1: Rectangle ABCD is given
Statement 2: segment AB ≅ segment DC because opposite sides of a rectangle are congruent
Statement 3: Angles ABC and DCB are both right angles by definition of a rectangle
Statement 4: Angles ABC and DCB are congruent because all right angles are congruent)
Statement 5:
Statement 6: Triangles ABC and DCB are congruent by SAS
Statement 7: segment AC ≅ segment DB by CPCTC
Which statement below completes Jimmy's proof?
segment AD ≅ segment AD (reflexive property of congruence)
segment AD ≅ segment AD (transitive property of congruence)
segment BC ≅ segment BC (reflexive property of congruence)
segment BC ≅ segment BC (transitive property of congruence)
Question 8(Multiple Choice Worth 1 points)
(02.03 MC)
triangle ADB, point C lies on segment AB and forms segment CD, angle ACD measures 90 degrees. 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 DC bisects segment AB, 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 segment DC bisects segment AB, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
If segment AD bisects segment AB, 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 segment AD bisects segment AB, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Question 9(Multiple Choice Worth 1 points)
(02.04 MC)
In triangle DEF, if m∠D = (2x)°, m∠E = (2x − 4)°, and m∠F = (x + 9)°, what is the value of x?
Triangle A B C is divided into two smaller triangles which are triangle A B D and D B C which share a common side B D. Point D lies on segment A C. Segment A D is congruent to segment C D.
If m∠BDC = 70°, what is the relationship between AB and BC?
AB = BC
AB < BC
AB > BC
AB + BC < AC
Question 11(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 12(Multiple Choice Worth 1 points)
(02.02 MC)
Rectangle is shown with vertices at negative 5 comma 1, negative 5 comma 3, negative 1 comma 3, and negative 1 comma 1.
What series of transformations would carry the rectangle onto itself?
(x + 0, y − 4), 180° rotation, reflection over the y-axis
(x + 0, y − 4), 180° rotation, reflection over the x‐axis
(x − 4, y + 0), 90° counterclockwise rotation, reflection over the x‐axis
(x − 4, y + 0), 90° counterclockwise rotation, reflection over the y-axis
Question 13(Multiple Choice Worth 1 points)
(02.02 LC)
Trapezoid ABCD is shown. A is at negative 5, 1. B is at negative 4, 3. C is at negative 2, 3. D is at negative 1, 1.
Trapezoid ABCD is rotated 90° clockwise. 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 14(Multiple Choice Worth 1 points)
(02.05 MC)
In triangle ABC shown below, side AB is 6 and side AC is 4:
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 3, and segment AE is 4.
Segment AD is 3, and segment AE is 2.
Segment AD is 12, and segment AE is 8.
Segment AD is 12, and segment AE is 4.
Question 15(Multiple Choice Worth 1 points)
(02.06 LC)
The figure below shows a quadrilateral ABCD. Sides AB and DC are equal 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 equal to side DC, and DB is the side common to triangles ABD and CDB. Angle ABD is congruent to angle CDB by Alternate Interior Angles. Therefore, the triangles ABD and CDB are congruent by SAS postulate. By CPCTC, angles DBC and ADB are congruent and sides AD and BC are congruent. Angle DBC and angle ADB ________. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel.
Which phrase best completes the student's proof?
are congruent by the AAS postulate
are congruent by the ASA postulate
form a pair of alternate interior angles that are congruent
form a pair of vertical angles that are congruent
1 answer
Here are the answers to your questions:
Question 1:
If triangle ABC is congruent to triangle DEF, which statement is not true?
Answer: ∠C ≅ ∠E (In congruent triangles, corresponding angles are congruent. Therefore, if ABC is congruent to DEF, ∠C would be congruent to ∠F, not ∠E.)
Question 2:
Which transformation can be used to show that ABCDE and its image are congruent?
Answer: Reflect ABCDE over the y-axis. (The points A′ and D′ show the polygon has been reflected over the y-axis.)
Question 3:
If quadrilateral PQRS is a rectangle, then which of the following is true?
Answer: segment PS ≅ segment QR (In rectangles, opposite sides are congruent.)
Question 4:
Which series of transformations will not map figure L onto itself?
Answer: (x − 4, y − 4), reflection over y = −x (This transformation will change the position of the figure rather than mapping it onto itself.)
Question 5:
What will be the location of T′ in the image trapezoid S′T′U′V′?
Answer: (12, 6) (To determine T', apply the same transformation applied to rectangle JKLM to trapezoid STUV.)
Question 6:
What would Ebony need to compare to make sure the triangles are congruent by AAS?
Answer: ∠EGF and ∠OMN (In AAS (Angle-Angle-Side), we require two angles and the included side to be congruent.)
Question 7:
Which statement below completes Jimmy's proof?
Answer: segment AD ≅ segment AD (reflexive property of congruence) (The reflexive property states that any geometric figure is congruent to itself.)
Question 8:
How could she prove that point D is equidistant from the jungle gym and monkey bars?
Answer: If segment DC bisects segment AB, 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 9:
What is the value of x in triangle DEF?
Question 10:
What is the relationship between AB and BC given that segment AD is congruent to segment CD?
Answer: AB > BC (If angle BDC is 70°, then by the triangle inequality, AB must be greater than BC.)
Question 11:
Which theorem can be used to fill in the missing reason for the proof?
Answer: Midsegment Theorem (Since DE is a midsegment, this translates the information needed to find angle AED.)
Question 12:
What series of transformations would carry the rectangle onto itself?
Answer: (x + 0, y − 4), 180° rotation, reflection over the x-axis (This combination of transformations would map the rectangle onto itself.)
Question 13:
What rule shows the input and output of the rotation, and what is the new coordinate of A′?
Answer: (x, y) → (−y, x); A′ is at (−1, −5) (This is the correct transformation for a 90° clockwise rotation.)
Question 14:
Which statement is needed to prove that segment DE is parallel to segment BC and half its length?
Answer: Segment AD is 3, and segment AE is 2. (This follows the midsegment theorem.)
Question 15:
Which phrase best completes the student's proof?
Answer: form a pair of alternate interior angles that are congruent (This follows from the fact that angles ABD and CDB are the same through the parallel lines.)
4 answers