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Wize High School Geometry Textbook (Common Core) > Congruent & Similar Triangles

Congruent Triangles (SSS)

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Congruent Triangles using SSS


In this theorem we only need to show information about the corresponding sides to get that the triangles are congruent.

Side Side Side (SSS) Theorem

If two triangles have a corresponding congruent sides, then the triangles are congruent.

More precisely if we have
  • CA‾≅FD‾,AB‾≅DE‾, and BD‾≅EF‾\overline{CA} \cong \overline{FD}, \overline{AB} \cong \overline{DE}, \text{ and } \overline{BD} \cong \overline{EF}
Then
  • △ABC≅△FDE\triangle{ABC} \cong \triangle{FDE}

Example:
Which pair of triangles can be considered congruent?

ANSWER:
The last two tringles labeled B and C are congruent. All of the marked sides are congruent. By the SSS theorem, these triangles are congruent.



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Construct a copy of a triangle (SSS)


Our goal in this construction is to copy a given triangle using all three sides. This is know as using side-side-side or SSS.

Using Technology


Begin with triangle △ABC\triangle ABC
  1. Draw a line A′D↔\overleftrightarrow{A'D}at the place where you want to build the new triangle.
  2. Use the compass tool to draw a circle with radius AB‾\overline{AB}centered at A′A'. Label the intersection of the circle and line as point B′B' .
  3. Use the compass tool to draw a circle with radius AC‾\overline{AC} centered at A′A'.
  4. Use the compass tool to draw a circle with radius BC‾\overline{BC} centered at B′B'. Label the intersection of the two circles as C′C'.
  5. Draw segments A′C′‾\overline{A'C'} and B′C′‾\overline{B'C'}.
From this we now have △ABC≅△A′B′C′\triangle ABC \cong \triangle A'B'C' using side-side-side.

Congruent Triangles

Jeff is working on making two frames in the shape of quadrilaterals. He figures if he makes the two frames using pieces of wood that are all the same length, that the two frames will be congruent.


Can Jeff conclude that the two frames will be congruent?

Congruent Triangles

In the diagram the two triangles are congruent via the SSS theorem. Find all the values of x which make them congruent. Enter in the smallest one first, separated by a comma.