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Segments
AD
and
BC
intersect at point O.
Prove that AC = BD,
m∠ABC=m∠BAD.

Sagot :

MrRoyal

There are several ways two triangles can be congruent.

  • [tex]\mathbf{AC = BD}[/tex] congruent by SAS
  • [tex]\mathbf{\angle ABC \cong \angle BAD}[/tex] congruent by corresponding theorem

In [tex]\mathbf{\triangle AOL}[/tex] and [tex]\mathbf{\triangle BOK}[/tex] (see attachment), we have the following observations

[tex]1.\ \mathbf{AO = DO}[/tex] --- Because O is the midpoint of line segment AD

[tex]2.\ \mathbf{BO = CO}[/tex] --- Because O is the midpoint of line segment BC

[tex]3.\ \mathbf{\angle AOB =\angle COD}[/tex] ---- Because vertical angles are congruent

[tex]4.\ \mathbf{\angle AOC =\angle BOD}[/tex] ---- Because vertical angles are congruent

Using the SAS (side-angle-side) postulate, we have:

[tex]\mathbf{AC = BD}[/tex]

Using corresponding theorem,

[tex]\mathbf{\angle ABC \cong \angle BAD}[/tex] ---- i.e. both triangles are congruent

The above congruence equation is true because:

  1. 2 sides of both triangles are congruent
  2. 1 angle each of both triangles is equal
  3. Corresponding angles are equal

See attachment

Read more about congruence triangles at:

https://brainly.com/question/20517835

View image MrRoyal
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