contestada

Analyze the figure and the two-column proof.


Triangles A F C and D E B overlap and intersect at point X. Point B of triangle D E B is on side A C of triangle A F C. Point C of triangle A F C is on side B D of triangle D E B. Angles A F C and B E D are right angles. Sides F A and E D are congruent. Line segments A B and C D are congruent.

Which statement/reason pair can be used when proving FC ≅ EB?

♣: Δ ≅ ΔAFC
♦:

Respuesta :

Answer:

1st one: DEB

2nd one: HL

Step-by-step explanation:

By segment addition property, the lengths of the hypotenuse side of both

triangles ΔAFC and ΔDEB are equal.

Response:

  • A statement/reason pair that can be used when proving [tex]\overline{FC}[/tex] ≅ [tex]\overline{EB}[/tex] is presented as follows: Statement; ΔAFC ≅ ΔDEB, reason; HL

Method used to obtain the above response

Please find attached the diagram representing the triangles

ΔAFC and ΔDEB overlap

Point B is located on side [tex]\mathbf{\overline{AC}}[/tex]

Point C is located on side [tex]\mathbf{\overline{BD}}[/tex]

∠AFC = ∠BED = 90°

[tex]\overline{FA}[/tex] ≅ [tex]\overline{ED}[/tex]

[tex]\overline{AB}[/tex] ≅ [tex]\overline{CD}[/tex]

A statement and reason pair that can be used to prove that [tex]\overline{FC}[/tex] ≅ [tex]\overline{EB}[/tex] is given as follows;

Statement [tex]{}[/tex]                                               Reasons

[tex]\overline{FA}[/tex] ≅ [tex]\overline{ED}[/tex] [tex]{}[/tex]                                               Given

ΔAFC and ΔDEB are right triangles[tex]{}[/tex]      Definition of right triangles

[tex]\overline{AB}[/tex] = [tex]\overline{CD}[/tex]   [tex]{}[/tex]                                               Definition of congruency

[tex]\overline{BC}[/tex] ≅ [tex]\overline{BC}[/tex]  [tex]{}[/tex]                                               Reflexive property

[tex]\overline{BC}[/tex] = [tex]\overline{BC}[/tex]  [tex]{}[/tex]                                                Definition of congruency

[tex]\overline{AB}[/tex] + [tex]\overline{BC}[/tex] = [tex]\overline{CD}[/tex] + [tex]\overline{BC}[/tex] [tex]{}[/tex]                              Substitution property

[tex]\overline{BD}[/tex] = [tex]\overline{AC}[/tex]  [tex]{}[/tex]                                   Substitution and segment addition property

ΔAFC ≅ ΔDEB  [tex]{}[/tex]                                Hypotenuse leg (HL) rule of congruency

[tex]\overline{FC}[/tex] ≅ [tex]\overline{EB}[/tex]  [tex]{}[/tex]                                              CPCTC

CPCTC is the acronym for Corresponding Parts of Congruent Triangles are Congruent

A statement/reason pair that can be used is therefore;

  • ΔAFC ≅ ΔDEB / Hypotenuse leg (HL) rule of congruency

Learn more about congruency theorem here:

https://brainly.com/question/2102943

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