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Conditions for Congruent Triangles

Author:Colleen Shallenberger

Intro (READ)

If two triangles are congruent, you know that all pairs of corresponding sides and angles are congruent. This means that there are 6 pairs of triangle parts that are congruent. But, two triangles will be congruent when less than 6 pairs of parts are known to be congruent--it depends on the parts. The big question for this activity is: what are the conditions that GUARANTEE congruent triangles? You will explore 7 different sets of conditions. Remember that congruent figures are exact copies of each other.
CONDITION SET 1: All corresponding sides are congruent. Will this guarantee that the triangles are congruent?

Will triangles be congruent if all the sides are congruent?

Select all that apply
  • A
  • B
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CONDITION SET 2: All angles are congruent. Will this guarantee that the triangles are congruent?

If all angles in one triangle are congruent to all the angles in another triangle, will this guarantee that the triangles are congruent?

Select all that apply
  • A
  • B
Check my answer (3)
CONDITION SET 3: Two angles and one side of a triangle are congruent to two corresponding angles and one side in the other triangle. Notice that the congruent angles are on the 'ends' of the one side.

Before exploring the applet, if two angles in one triangle are congruent to two angles of the other, will the third angle pair also be congruent?

Select all that apply
  • A
  • B
  • C
Check my answer (3)

If two angles and the side in-between them are congruent to two corresponding angles and the corresponding side in another triangle, will this guarantee the triangles are congruent?

Select all that apply
  • A
  • B
Check my answer (3)
CONDITION SET 4: Two angles and one side of a triangle are congruent to the corresponding angles and side of another triangle. Note: the congruent side is NOT in-between the two angles.

If two angles and a side that is not in-between in one triangle are congruent to the corresponding angles and side in another triangle, will this guarantee the triangles are congruent?

Select all that apply
  • A
  • B
Check my answer (3)
CONDITION SET 5: Two sides and one angle, not in-between the sides, of one triangle are congruent to two corresponding sides and angle in another triangle.

Notice that two sides and one angle of the top triangle are congruent to two sides and one angle of the bottom. Explore the applet by changing the value of r and/or clicking to show the 2nd triangle.

If two sides and one angle, not in-between the sides, are congruent to two corresponding sides and one angle in another triangle, will this guarantee the triangles are congruent?

Select all that apply
  • A
  • B
Check my answer (3)
CONDITION SET 6: Two sides and the angle in-between the sides of one triangle are congruent to the corresponding sides and included angle of another triangle.

Move the vertices of the blue triangle to see if the outcome changes.

If two sides and the angle in-between of one triangle are congruent to two corresponding sides and angle in another triangle, does this guarantee the triangles are congruent?

Select all that apply
  • A
  • B
Check my answer (3)
CONDITION SET 7: In RIGHT TRIANGLES, the hypotenuse and one leg of a right triangle is congruent to the hypotenuse and leg of another right triangle.

If the hypotenuse and one leg of a RIGHT triangle is congruent to the hypotenuse of another right triangle, does this guarantee the triangles are congruent?

Select all that apply
  • A
  • B
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SUMMARY

Which of the following conditions/situations GUARANTEE congruent triangles? Check all that are true.

Select all that apply
  • A
  • B
  • C
  • D
  • E
  • F
  • G
Check my answer (3)

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