SAS or SSS?

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 17 of 60.

Before you pick a rule, count what you have. Three pairs of sides is SSS. Two pairs of sides with the angle between them is SAS. Two pairs of sides and an angle anywhere else is SSA, which proves nothing.

$Kite KLMN with both pairs of sides ticked and the diagonal KM$

In this kite the ticks give KL = KN and ML = MN, and KM is shared: three pairs of sides, so SSS. If the ticks on KL and KN were missing and the angles at M were marked instead, you would have ML = MN, the shared KM and the angle at M between them, so SAS.

Challenge

In kite ABCD only AB and AD are ticked, and the diagonal AC splits the angle at A into two angles marked equal. The statements of the proof are written. Give each its reason, then press Check.

Try it yourself

$Write the proof$

Write the proof

All lessons in Congruence & Proof

2Congruent Triangles

Same Size, Same Shape What Congruence Gives Recap: Matching Parts

5ASA and AAS

The Side Between The ASA Rule The AAS Rule ASA or AAS?Recap: ASA and AAS

8Proofs with Vertical Angles

Vertical Angles in Proofs The Bowtie Bowtie with ASA Linear Pairs in Proofs Recap: Vertical Angles

11Similarity Proofs