MAFS.912.G-CO.2.6

  1. Reflections and Equilateral Triangles
    SupposeABCis an equilateral triangle:
  1. Describe three reflections of the plane which preserve triangle.
  2. Show that the three lines of symmetry from part (a) are the perpendicular bisectors of segmentsand.
  1. Reflections and Isosceles Triangles
    Supposeis an isosceles triangle with sidecongruent to sideas pictured below:

Also pictured above is the midpointof side. Letdenote lineand letdenote the map of the plane determined by reflection about the line.

  1. Show that and.
  2. Using part (a) show thatmaps the triangleto itself.
  3. Supposeis a triangle in the plane and that there is a lineso that reflection aboutMmaps triangleto itself. Show that triangleis an isosceles triangle.

MAFS.912.G-CO.2.7

  1. Given with vertices , , and with vertices , , , use the definition of congruence in terms of rigid motion to show that . Describe each rigid motion in terms of coordinates (x, y).
  1. Given: in which , , , .
  1. Use the definition of congruence in terms of rigid motion to prove.

MAFS.912.G-CO.2.8

  1. In the diagram, , and .

Using rigid motion, explain in detail, why triangle ABC must be congruent to triangle DEF

  1. In the diagram, , and .

Using rigid motion, explain in detail, why triangle ABC must be congruent to triangle DEF.

MAFS.912.G-SRT-2.5

1. In the picture below, line segments AD and BC intersect at X. Line segments AB and CD are drawn, forming two triangles AXB and CXD. In each part a-d below, some additional assumptions about the picture are given.

In each problem, determine whether the given assumptions are enough to prove that the two triangles are similar, and if so, what the correct correspondence of vertices is.

If the two triangles must be similar, prove this result by describing a sequence of similarity transformations that maps one variable to the other. If not explain why not.

a. The lengths of AX and AD satisfy the equation 2AX = 3XD.

b. The lengths AX, BX, CX, and DX satisfy the equation

c. Lines AB and CD are parallel.

d. XAB is congruent to angle XCD .

MAFS.912.G-SRT-2.5

2 In trianglesABCandDEFbelow(∠A) =m (∠D),(∠B)=(∠E)

andAB=DE.

  1. Find a sequence of translations, rotations, and reflections which maps△ABCto△DEF.
  1. After working on problem (a), Melissa says

Sincem(∠A)=m(∠D)andm(∠B)=m(∠E)then I also know thatm(∠C)=m(∠F). So these triangles share all three angles and this is enough to know that they are congruent. I don't need to be told that|AB|=|DE|.

  1. Is Melissa correct that(∠C)=(∠F)? Explain.
  2. Is she right that two triangles sharing three pairs of congruent angles are always congruent? Explain.