Respuesta :

Answer:


Step-by-step explanation:

Angle 4 = angle 1 and angle 3 =angle 2        Corresponding angles for two        parallel lines BD and AE

Triangle AED ||| BDE                                       Angle angle congruent

...                                                                       By compendo and dividendo

Thus proved

Since two lines are parallel we have corresponding angles equal and also

sides will be proportional in similar triangles

Using that and adjusting compendo and dividendo we get the desired result

akposevictor

The missing phrase or expression that completes the proof are:

  • First box: Corresponding Angles Postulate
  • Second box: [tex]\triangle ACE \cong \triangle BCD[/tex]
  • Third box: Segment Addition Postulate

From the diagram given, <4 and <1 are corresponding angles, so also <3 and <2.

Corresponding angles are always equal/congruent.

  • Therefore, the reason that justifies [tex]\angle 4 \cong \angle 1, \angle 3 \cong \angle 2[/tex] is: Corresponding Angles Postulate

Since [tex]\triangle ACE $ and $ \triangle BCD[/tex] both have two pairs of congruent angles, therefore, based on the Angle-Angle Similarity postulate:

  • [tex]\triangle ACE \cong \triangle BCD[/tex].

Also, the segment addition postulate states that if a segment is consist of two small segments, its length will be the sum of the two small segments.

Therefore, the reason that justifies why CA = CB + BA, and CE = CD + DE is:

  • segment addition postulate

Learn more here:

https://brainly.com/question/7576859

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