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Exploring Congruent Triangles

Author:Heather O'Brien, mangat
Topic:Geometry
  • Are there any shortcuts of proving triangles congruent?
  • What corresponding triangle parts need to be congruent in order to show that two triangles are congruent?
These applets will allow you to explore whether triangle relationships (SSS, AAA, SAS, HL, SSA, ASA, AAS) force triangles to be congruent or not.

Side-Side-Side triangles (SSS)

If three sides of one triangle are congruent to three sides of second triangle, are the triangles congruent?

Question

Use the exploration from the above applet to write if the triangles are congruent in SSS case.

Angle- Angle- Angle (AAA)

If three angles of one triangle are congruent to three angles of another triangles, then are the triangles congruent?

Question

Use the exploration from the above applet to write if the triangles are congruent in AAA case. If they are not congruent, then in what case will they be congruent?

Side-Angle-Side (SAS)

If two sides and included angle of one triangle are congruent to two sides and included angle of other triangle, then are the triangles congruent?

SAS triangle Congruence

Question

Use the exploration from the above applet to write if the triangles are congruent in SAS case.

Hypotenuse-Leg (HL)

If hypotenuse and a leg of one triangle are congruent to hypotenuse and leg of second triangle, are the triangles congruent?

HL congruence

Question

Use the exploration from the above applet to write if the triangles are congruent in HL case.

Side-Side-Angle (SSA)

If two sides and non included angle of one triangle are congruent to two sides and a non included angle of another triangle, are the triangles congruent?

Question

Use the exploration from the above applet to write if the triangles formed are always are congruent in SSA case.

Angle- Side- Angle (ASA)

If two angles and included side of one triangle are congruent to two angles and included side of another triangle, then are the triangles congruent?

ASA

Question

Use the exploration from the above applet to write if the triangles are congruent in ASA case.

Angle-Angle-Side (AAS)

If two angles and non included side of one triangle are congruent to two angles and non included side of another triangle, then are the triangles congruent?

AAS congruence

Question

Use the exploration from the above applet to write if the triangles are congruent in AAS case.

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