Math Problem Statement

Question 2 (Multiple Choice Worth 1 Points) (02.03 MC)

If ΔABC ≅ ΔEDF where the coordinates of A(−1, 1), B(2, 4), and C(3, 1), what is the measure of EF? 3 3.2 4 4.6 Question 3 (Multiple Choice Worth 1 Points) (02.03 MC)

Are triangles ABC and ADC congruent?

triangles ABC and ADC share segment AC, triangle ABC has one dash on side AB and two dashes on side BC, triangle ADC has one dash at side AD and two dashes on side DC Yes, by SSS Yes, by ASA Yes, by SAS Not enough information Question 4 (Multiple Choice Worth 1 Points) (02.03 MC)

What additional information would you need to prove that ΔABC ≅ ΔDEF by ASA?

Triangle ABC and triangle DEF are drawn with angles B and E marked congruent and angles C and F marked congruent. segment AB ≅ segment DE segment BC ≅ segment FE segment AB ≅ segment FE segment BC ≅ segment EF Question 5 (Multiple Choice Worth 1 Points) (02.03 LC)

If ΔFGH ≅ ΔIJK, which segment is congruent to segment FH? segment IK segment JK segment IJ segment FG Question 6 (Multiple Choice Worth 1 Points) (02.03 MC)

If a reflection takes triangle CAT to C′A′T′, what is A′C′?

triangle CAT with vertex A at negative 2 comma 1, vertex T at negative 1 comma 4 and vertex C at 0 comma 0, side AT has a measure of square root of 10 units, side TC has a measure of square root of 17 units, and side AC has a measure of square root of 5 units 3 4 square root of 5 Cannot be determined Question 7 (Multiple Choice Worth 1 Points) (02.03 MC)

Slade draws triangle PQR. He then constructs a perpendicular bisector from vertex P that intersects side QR at point T. What can Slade conclude, based on his drawing? QT = RT TP = RQ PQ = RQ PT = PQ Question 8 (Multiple Choice Worth 1 Points) (02.03 MC)

What coordinate for F would make triangle ABC and triangle DEF congruent?

Triangle ABC is shown. For triangle ABC, A is at 0, 3, B is at negative 1, 2, C is at 2, 3. Two other coordinates are shown. D is at negative 1, 0, E is at 1, negative 2. (−3, −3) (−3, −2) (−2, −3) (−2, −2) Question 9 (Multiple Choice Worth 1 Points) (02.03 LC)

If ΔABC ≅ ΔFDE, which of the following statements is true? ∠A ≅ ∠E ∠B ≅ ∠F ∠A ≅ ∠D ∠B ≅ ∠D Question 10 (Multiple Choice Worth 1 Points) (02.03 LC)

The grid shows Figure Q and its image Figure Q′ after a transformation.

Figure Q is a pentagon drawn on a coordinate grid with vertices in clockwise order at point 2 comma 4, point 3 comma 7, point 7 comma 5, point 5 comma 4, and point 4 comma 2. Figure Q’ is a pentagon drawn with vertices in clockwise order at point negative 2 comma 4, point negative 4 comma 2, point negative 7 comma 3, point negative 5 comma negative 7, and point negative 4 comma 5.

Which of the following transformations could be used to prove that Figure Q and Figure Q′ are congruent? Clockwise rotation of 180° about the origin Counterclockwise rotation of 90° about the origin Clockwise rotation of 90° about the origin Counterclockwise rotation of 270° about the origin

Solution

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Math Problem Analysis

Mathematical Concepts

Congruent Triangles
Coordinate Geometry
Reflection and Transformations
Triangle Theorems

Formulas

Distance formula: d = √((x2 − x1)^2 + (y2 − y1)^2)

Theorems

SAS Congruence Theorem
ASA Congruence Theorem
Reflection Theorem

Suitable Grade Level

Grades 8-10