Lesson 1

Congruent Parts, Part 1

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Problem 1

When rectangle \(ABCD\) is reflected across line \(EF\), the image is \(DCBA\). How do you know that segment \(AB\) is congruent to segment \(DC\)?

Rectangle ABCD is reflected across line EF creating rectangle CDEF.
A:

A rectangle has 2 pairs of parallel sides.

B:

Any 2 sides of a rectangle are congruent.

C:

Congruent parts of congruent figures are corresponding.

D:

Corresponding parts of congruent figures are congruent.

Solution

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Problem 2

Triangle \(FGH\) is the image of isosceles triangle \(FEH\) after a reflection across line \(HF\). Select all the statements that are a result of corresponding parts of congruent triangles being congruent.

\(\overline{FE} \cong \overline{HE}\)

Triangle FGH is the image of isosceles triangle  FEH after a reflection across line HF.
A:

\(EFGH\) is a rectangle.

B:

\(EFGH\)  has 4 congruent sides.

C:

Diagonal \(FH\) bisects angles \(EFG\) and \(EHG\).

D:

Diagonal \(FH\) is perpendicular to side \(FE\).

E:

Angle \(FEH\) is congruent to angle \(FGH\).

Solution

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Problem 3

Reflect right triangle \(ABC\) across line \(BC\). Classify triangle \(ACA’\) according to its side lengths. Explain how you know.

Triangle A B C. Angle B is a right angle.

Solution

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Problem 4

Triangles \(FAD\) and \(DCE\) are translations of triangle \(ABC\)

Large triangle BFE has small triangle ADC at its midpoints.

Select all the statements that must be true.

A:

Points \(B\), \(A\), and \(F\) are collinear.

B:

The measure of angle \(BCA\) is the same as the measure of angle \(CED\).

C:

Line \(AD\) is parallel to line \(BC\).

D:

The measure of angle \(CED\) is the same as the measure of angle \(FAD\).

E:

The measure of angle \(DAC\) is the same as the measure of angle \(BCA\).

F:

Triangle \(ADC\) is a reflection of triangle \(FAD\).

Solution

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(From Unit 1, Lesson 21.)

Problem 5

Triangle \(ABC\) is congruent to triangles \(BAD\) and \(CEA\).

Trapezoid DECB base BC and point A midpoint of DE making triangle ABC.
  1. Explain why points \(D\), \(A\), and \(E\) are collinear.
  2. Explain why line \(DE\) is parallel to line \(BC\).

Solution

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(From Unit 1, Lesson 21.)

Problem 6

  1. Identify a figure that is the result of a rigid transformation of quadrilateral \(ABCD\).  
  2. Describe a rigid transformation that would take \(ABCD\) to that figure.
6 quadrilaterals.

Solution

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(From Unit 1, Lesson 18.)