Lesson 4 Congruent Triangles Solidify Understanding

Ready

Given the figures with congruent angles and sides marked in each sketch, first list the parts of the figures that are corresponding and congruent (for example, in problem 1, ). Then determine if a reflection occurred as part of the sequence of transformations that was used to create the image.

1.

triangle ABC is transformed to SRT

Congruencies

Reflected? Yes or No

2.

quadrilateral EFGH is transformed to WXYZ

Congruencies:

Set

Use the congruence markings to determine whether the triangles are congruent, similar, or neither. State the triangle congruence criterion connected to the pair of triangles that are congruent or similar.

3.

Two triangles marked with one tic on one side, two tics on another, and three tics on the third side.

4.

Two triangles with angles marked with one arc, two arcs, and three arcs.

5.

Two triangles with two sides marked congruent and an excluded angle marked congruent.

6.

Two triangles with two sides marked congruent with the included angle marked congruent.

7.

Two triangles with two angles marked congruent and the excluded side marked congruent.

8.

Two triangles with two sides marked congruent with the included angle marked congruent.

9.

Provide a sequence of transformations that can be used to justify that triangle is congruent to triangle . Explain how the congruent features indicated on the triangles and the transformations prove that the triangles are congruent.

Triangle VWZ with angle W with one arc, angle Z with two arcs, and line segment WV with one tic mark. Triangle LNM with angle N with one arc, angle M with two arcs, and line segment NL with one tic mark.

10.

Describe a sequence of transformations and a triangle congruence criterion to justify that triangle is congruent to triangle .

Triangle DFE with angle F marked with one arc, line segment FE with one tic and line segment FD with two tics. Triangle ZXY with angle X with one arc, line segment XY with one tic and line segment XZ with two tics.

Use the given congruence statements to draw and label two triangles so that the corresponding parts are congruent.

11.

12.

Go

Solve each equation for .

13.

14.

15.

16.

Use a compass and a straightedge to construct each figure.

17.

Construct an equilateral triangle with the given segment as one of its sides.

a line segment

18.

Construct a rhombus with as one side of the rhombus and angle as one of the angles of the rhombus.

Angle A with one side Ray A and the other side line segment AB