Kellis Segment One Practice Exam- 5.09

Trapezoid ABCD is rotated 180 degrees about the origin and then reflected over the x-axis, followed by a reflection over the y-axis. What is the location of point A after the transformations are complete? A (-5, 1) - (5, -1) - (-5, -1) - (5, 1) - (-5, 1)

(-5, 1)

The following is an incomplete flowchart proving that the opposite angles of parallelogram JKLM are congruent: Which reasons can be used to fill in the numbered blank spaces? - 1. Alternate Interior Angles Theorem 2. Corresponding Angles Theorem - 1. Corresponding Angles Theorem 2. Alternate Interior Angles Theorem - 1. Alternate Interior Angles Theorem 2. Same-Side Interior Angles Theorem - 1. Corresponding Angles Theorem 2. Same-Side Interior Angles Theorem

1. Alternate Interior Angles Theorem 2. Corresponding Angles Theorem

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 angle ADE is 28°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 62°: Which statement and reason can be used to fill in the numbered blank spaces? - 1. Base Angle Theorem 2. Corresponding angle are congruent 3. Measure of angle AED is 28°. -1. Alternate interior angles are congruent 2. Base Angle Theorem 3. Measure of angle AED is 62°. - 1. Corresponding angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 28°. - 1. Corresponding angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 62°.

1. Corresponding angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 62°.

Peter reflected parallelogram ABCD across the y-axis. If angle A is 115° and angle B is 65°, what is the degree measurement of angle A'? - 65° - 50° - 115° - 180°

115°

In the figure below, triangle ABC is similar to triangle PQR: AB- 12 BC- 11.5 QR- 34.5 What is the length of side PQ? - 12 - 35 - 33 - 36

36

Gary is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: He starts with the assumption that segment DE is parallel to segment BC. Which inequality will he use to contradict the assumption? - 4:10 ≠ 6:14 - 4:6 ≠ 6:14 - 4:10 ≠ 6:8 - 4:14 ≠ 6:10

4:10 ≠ 6:14

Which statement is true about a line and a point? - A point and a line have length as a dimension to measure - A point is a location, and a line has many points located on it - A line and a point cannot lie on the same plane - A line and point cannot be collinear

A point is a location, and a line has many points located on it.

Stella is using her compass and straightedge to complete a construction of a polygon inscribed in a circle. Which polygon is she in the process of constructing? - An isosceles triangle - A square - A regular pentagon - A regular hexagon

A regular hexagon

What construction does the image below demonstrate? - A square circumscribed about a circle - A square inscribed in a circle - The circumcenter of a square - The incenter of a square

A square inscribed in a circle

Triangle QRS has been translated to create triangle Q'R'S'. RS = R'S' = 2 units, angles S and S' are both 28 degrees, and angles R and R' are both 32 degrees. Which postulate below would prove the two triangles are congruent? - SSS - SAS - ASA - AAS

ASA

Triangle ABC is dilated to create triangle DEF on a coordinate grid. You are given that angle A is congruent to angle D. What other information is required to prove that the two triangles are similar? - Angle B is congruent to angle D. - Segments AB and DE are congruent. - Angle B is congruent to angle E. - Segment AC is congruent to segment DF, and segment BC is congruent to segment EF.

Angle B is congruent to angle E.

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 SAS postulate. By CPCTC, angles DBC and BDA are congruent and sides AD and BC are congruent. Angle DBC and angle BDA form a pair of vertical angles which are congruent. Therefore, AD is parallel and equal to BC. Quadrilateral ABCD is a parallelogram because its opposite sides are equal and parallel. Which statement best describes a flaw in the student's proof? - Triangles ABD and BCD are congruent by the SSS postulate. - Triangles ABD and BCD are congruent by the AAS postulate. - Angle DBC and angle ADB form a pair of corresponding angles which are congruent. - Angle DBC and angle ADB form a pair of alternate interior angles which are congruent.

Angle DBC and angle ADB form a pair of alternate interior angles which are congruent.

The grid below shows figure Q and its image figure Q' after a transformation: Which transformation was applied on figure Q? - Counterclockwise rotation of 90° about the origin - Counterclockwise rotation of 270° about the origin - Clockwise rotation of 90° about the origin - Clockwise rotation of 180° about the origin

Clockwise rotation of 180° about the origin

Rectangle ABCD is similar to rectangle EFGH. Side CD is proportional to side ___. - EF - FG - GH - HE

GH

If triangle GHI is congruent to triangle JKL, which statement is not true? - HI ≅ KI - ∠G ≅ ∠J - GH ≅ KL - ∠I ≅ ∠L

GH ≅ KL

The figure below shows a square ABCD and an equilateral triangle DPC: Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC: 1. In triangles APD and BPC; DP = PC- Sides of equilateral triangle DPC are equal 2. In triangles APD and BPC; AD = BC- Sides of square ABCD are equal 3. In triangles APD and BPC; angle ADP = angle BCP- Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 60° 4. Triangles APD and BPC are congruent- SAS postulate - He writes the measure of angles ADP and BCP as 60° instead of 45°. - He uses the SAS postulate instead of AAS postulate to prove the triangles congruent. - He writes the measure of angles ADP and BCP as 60° instead of 30°. - He uses the SAS postulate instead of SSS postulate to prove the triangles congruent.

He writes the measure of angles ADP and BCP as 60° instead of 30°.

Which step should be used to prove that point P is equidistant from points R and Q? - If any one side and any one common angle are equal in triangles PQR and PRS, then their corresponding sides are also equal. - If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal. - In triangles PQR and PQS, if one side and one angle are equal, then their corresponding sides and angles are also equal. - In triangles PRS and PQS, all three angles are equal.

If two sides and one included angle are equal in triangles PQS and PRS, then their third sides are equal.

A student made the following chart to prove that AB2 + BC2 = AC2: 1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BDC and Angle BCA = Angle DCB 2. BC2 = AC x DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC 3. Triangle ABC is similar to triangle ADB 3. Angle ABC = Angle BAD and Angle BAC = Angle ABD 4. AB2 = AC x AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ABD 5. AB2 + BC2 = AC x AD + AC x DC = AC (AD + DC) 5. Adding Statement 2 and Statement 4 6. AB2 + BC2 = AC2 6. AD + DC = AC - Justification 4 should be "AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD." - Justification 1 should be "Angle ABC = Angle BCD and Angle BCA = Angle DBC." - Justification 2 should be "BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC." - Justification 3 should be "Angle ABC = Angle ADB and Angle BAC = Angle DAB."

Justification 3 should be "Angle ABC = Angle ADB and Angle BAC = Angle DAB."

Are the two triangles below similar? ∠G= 46 ∠I= 27 ∠K= 108 ∠L= 27 - Yes; they have congruent corresponding angles. - No; they do not have congruent corresponding angles. - Yes; they have proportional corresponding sides. - No; they do not have proportional corresponding sides.

No; they do not have congruent corresponding angles.

Alice is designing a book shelf. The segment LQ represents the base of the book shelf. Alice wants to construct a line to represent a rack passing through R and parallel to side LQ. She uses a straightedge and compass to complete some steps of the construction, as shown below: Which of these is likely to be her next step in constructing the rack parallel to LQ? - Place the compass at S, and adjust its width to point P. - Without changing the width of the compass, fix the compass at P, and draw an arc. - Without changing the width of the compass, place the compass at S or P, and draw an arc similar to the one drawn. - Place the compass at N, and adjust the width to a length that is greater than the length of segment NS.

Place the compass at S, and adjust its width to point P.

Which transformation will map figure K onto figure K'? - Reflection across the x-axis - Vertical translation of 6 units - Vertical translation of 11 units - Reflection across the y-axis

Reflection across the x-axis

The figure shows triangle ABC with medians AF, BD, and CE. Segment AF is extended to H in such a way that segment GH is congruent to segment AG, as shown below: Which conclusion can be made based on the given conditions? - Segment GF is parallel to segment EB. - Segment EG is parallel to segment BH. - Segment BH is congruent to segment HC. - Segment EG is congruent to segment GD.

Segment EG is parallel to segment BH.

If triangle MNO is similar to triangle PQR, which statement is true about the two triangles? - Segment NO is proportional to segment QR, and angles M and P are congruent. - Segment MN is congruent to segment PQ, and angles O and R are congruent. - Segment NO is proportional to segment QR, and angles M and P are proportional. - Segment MN is congruent to segment PQ, and angles O and R are proportional.

Segment NO is proportional to segment QR, and angles M and P are congruent.

Rafael wrote the statements shown in the chart below: 1. If a point lies outside a line, then exactly one plane contains both the line and the point 2. If two points lie in a plane, then the line joining them lies in that plane. Which option best classifies Rafael's statements? - Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact. - Statement 1 and Statement 2 are postulates because they are true facts. - Statement 1 is a postulate because it is a true fact, and Statement 2 is a theorem because it can be proved. - Statement 1 and Statement 2 are theorems because they can be proved.

Statement 1 is a theorem because it can be proved, and Statement 2 is a postulate because it is a true fact.

Polygon PQRST shown below is dilated with a scale factor of 3, keeping vertex P as the center of dilation: Which statement about polygon PQRST and its image after dilation, polygon P'Q'R'S'T', is correct? - The lengths of side RQ and side R'Q' are in the ratio 1:3. - The length of diagonal RT is equal to the length of diagonal R'T'. - The measures of angle S and angle S' are in the ratio 1:3. - The length of side PQ is equal to the length of side P'Q'.

The lengths of side RQ and side R'Q' are in the ratio 1:3.

Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: S(2, 8) R(4, 8) P(2, 2) Q(4, 2) M(5, 5) L(6, 5) J(5, 2) K(6, 2) Which statement is correct? - The two tiles are not similar because is 5:1 and is 2:3. - The two tiles are similar because is 1:3 and is also 1:3. - The two tiles are similar because is 3:2 and is also 3:2. - The two tiles are not similar because is 1:6 and is 1:3.

The two tiles are similar because is 1:3 and is also 1:3.

Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coordinate plane as kites BRAD and KELY, respectively: Which statement is correct about the two kites? - They are similar because BR:DB is 1:2 and KE:YK is 1:3 - They are similar because BR:DB is 1:2 and KE:YK is 1:2 - They are not similar because BR:DB is 1:2 and KE:YK is 1:3 - They are not similar because BR:DB is 1:3 and KE:YK is 1:2

They are not similar because BR:DB is 1:2 and KE:YK is 1:3

Triangle CAT is translated using the rule (x, y) → (x − 3, y + 4) to create triangle C'A'T'. If a line segment is drawn from point C to point C' and from point A to point A', which statement would best describe the line segments drawn? - They share the same midpoints. - They are diameters of concentric circles. - They are perpendicular to each other. - They are parallel and congruent.

They are parallel and congruent.

Based on the figure, which pair of triangles is congruent by the Side Angle Side Postulate? - Triangle ACD and Triangle ACE - Triangle AEC and Triangle DEC - Triangle ABE and Triangle ACE - Triangle AEB and Triangle DEC

Triangle AEB and Triangle DEC

Chelsea drew two parallel lines KL and MN intersected by a transversal PQ, as shown below: Which fact would help Chelsea prove that the measure of angle KRP is equal to the measure of angle MSR? - When angles KRS and MSR are equal to angle RSN, the angles KRP and MSR are congruent. - When angles KRP and KRS are equal to angle LRS, the angles KRP and MSR are congruent. - When angle LRS is equal to angle KRP and angles LRS and RSN are complementary, angle KRP and angle MSR are congruent. - When angle LRS is equal to both the angles KRP and MSR, angle KRP and angle MSR are congruent to each other.

When angle LRS is equal to both the angles KRP and MSR, angle KRP and angle MSR are congruent to each other.

Are the following rectangles similar? AB-5 BC-25 EF-3 FG-15 - Yes; the corresponding angles are congruent. - No; the corresponding angles are not congruent. - Yes; the corresponding sides are proportional. - No; the corresponding sides are not proportional.

Yes; the corresponding sides are proportional.

Triangle ABC is similar to triangle PQR, as shown below: Which equation is correct? - c/a=q/r - c/b=a/r - b/q=a/p - c/q=a/r

b/q=a/p

Parallelogram FGHI on the coordinate plane below represents the drawing of a horse trail through a local park: In order to build a scale model of the trail, the drawing is enlarged on the coordinate plane. If two corners of the trail are at point A(−2, 7) and point D(−10, −1), what is another point that could represent a corner of the trail? (G) - (10, 7) - (14, 7) - (12, 7) - (8, 7)

(10, 7)

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, as shown below: S(9, -6) T (9, -2) U (7, -2) V (6, -5) What will be the location of U' in the image trapezoid S'T'U'V'? - (16, −2) - (14, −2) - (14, 1) - (16, 1)

(16, 1)

Dora is writing statements as shown below to prove that if segment ST is parallel to segment RQ, then x = 12: 1.Segment ST is parallel to segment QR - Given 2. Angle QRT is congruent to angle STP- Corresponding angles formed by parallel lines and their transversal are congruent. 3. Angle SPT is congruent to angle QPR- Reflective property of angles 4. Triangle SPT is similar to triangle QPR- Angle-angle similarity postulate 5. ? - Corresponding sides of similar triangle are in proportion - (3x + 24):3x = 85:51 - (3x + 24):85 = 3x:51 - (3x + 24):51 = 3x:85 - 34:24 = 3x:51

(3x + 24):3x = 85:51

Kite ABCD is reflected over the line y = x. What rule shows the input and output of the reflection, and what is the new coordinate of A'? A (-7, 2) - (x, y) → (y, x); A' is at (2, −7) - (x, y) → (−x, y); A' is at (7, 2) - (x, y) → (−x, −y); A' is at (7, −2) - (x, y) → (y, −x); A' is at (2, 7)

(x, y) → (y, x); A' is at (2, −7)

Figure EFGH on the grid below represents a trapezoidal plate at its starting position on a rotating surface: The plate is rotated 90° about the origin in the counterclockwise direction. In the image trapezoid, what are the coordinates of the endpoints of the side congruent to side EH? E (-4, 8) H (-2, 5) - (8, 4) and (5, 2) - (4, −8) and (2, −5) - (−8, −4) and (−5, −2) - (−8, −4) and (−5, −7)

(−8, −4) and (−5, −2)

The figure below shows segments KL and MN which intersect at point P. Segment KM is parallel to segment LN: Which of these facts is used to prove that triangle KMP is similar to triangle LNP? - Angle KMP is congruent to angle LNP because they are vertical angles. - Angle KMP is congruent to angle LNP because they are alternate interior angles. - Angle KPM is congruent to angle LPN because alternate exterior angles are congruent. - Angle KPM is congruent to angle LPN because corresponding angles are congruent.

Angle KMP is congruent to angle LNP because they are alternate interior angles.

What set of reflections would carry parallelogram ABCD onto itself? A (-5, 1) B (-4, 3) C (-1, 3) D (-2, 1) - x-axis, y=x, y-axis, x-axis - x-axis, y-axis, x-axis - y-axis, x-axis, y-axis, x-axis - y=x, x-axis, x-axis

y-axis, x-axis, y-axis, x-axis