Final: The Height Bisects

Part of the Congruence & Proof section of Coddy's Geometry journey. Lesson 59 of 60.

In △ABC the ticks show BA = BC. D lies on AC, and you are given that BD ⊥ AC.

Prove that BD bisects the angle at B. The perpendicular is written as a given, not drawn with squares, so you will have to turn it into right angles yourself.

Challenge

In △ABC the ticks show BA = BC, and you are given BD ⊥ AC with D on AC. Prove that BD bisects ∠ABC, 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

3SSS

Three Sides Fix It The SSS Rule A Shared Side SSS with a Shared Side Recap: SSS

6HL for Right Triangles

Hypotenuse and Legs The HL Rule Why HL Works HL with a Shared Leg Recap: HL

9Proofs with Parallel Lines

Parallel Angles as Reasons Alternate Angles in a Proof Corresponding Angles in Proofs Parallel or Not?Recap: Parallel Proofs

12Final Challenges

Final: The Kite Diagonals Final: Overlapping Triangles Final: Enough to Find It?Final: The Height BisectsFinal: The Roof Frame