Question

Given: AD¯¯¯¯¯ is an altitude.

Prove: AB^2 + AC^2 = CB^2

https://i.postimg.cc/G3GThF19/8124551-GA-GMT-IT-03-NP004-132.png

Drag and drop a reason into each box to correctly complete the two-column proof.

Statement Reason

AD¯¯¯¯¯ is an altitude, and ∠BAC ​ is a right angle. Given

∠ADB ​and ∠ADC are right angles. Definition of altitude

∠BAC≅∠BDA
∠BAC≅∠ADC All right angles are congruent.

∠B≅∠B
∠C≅∠C Reflexive Property of Congruence

△ABC∼△DBA _____________________
△ABC∼△DAC

AB/BD = CB/AB Polygon Similarity Postulate

AB^2 = (CB) (BD) Cross multiply and simplify.

AC/DC = CB/AC _____________________

AC^2 = (CB) (DC) Cross multiply and simplify.

AB^2 + AC^2 = AB^2 + (CB) (DC) ___________________

AB^2 + AC^2=(CB) (BD) + (CB) (DC) Substitution Property of Equality

AB^2 + AC^2 = (CB) (BD + DC) Distributive Property of Equality

BD + DC = CB Segment Addition Postulate

AB^2 + AC^2 = CB^2 Substitution Property of Equality

AA Similarity Postulate

SSS Similarity Postulate

Congruent Angle Postulate

Polygon Similarity Postulate

Substitution Property of Equality

Addition Property of Equality