Given: ad = bc and bcd = adc
prove: de = ce

According to AD=BC So AC=BD

Step-by-step explanation:

AD = BC and angle ADC = angle BCD

we have to prove AC = BD

let's see ∆ADC and ∆BCD

AD = BC [ given ]

angle ADC = angle BCD [ given ]

CD = CD

from S - A - S

∆ADC congruence ∆BCD

By addition property, equal areas subtracted from congruent triangles, form two other congruent triangles

≅ by Congruent Parts of Congruent Triangles are Congruent, (CPCTC)

The reason the above proof is correct is given as follows;

The given parameters are;

≅ and ∠BCD ≅ ∠ADC

Required:

Prove: ≅

A two column proof is presented as follows;

Statement                                  Reason

≅                                   Given

∠BCD ≅ ∠ADC                          Given

≅                                  Reflective property

ΔADC ≅ ΔBDC                         SAS rule of congruency

≅                                  Reflective property

ΔABD ≅ ΔABC                         SSS rule of congruency

ΔABD = ΔABE + ΔAED             Addition property

ΔABC = ΔABE + ΔBEC             Addition property

Therefore;

ΔAED = ΔBEC                           By converse of addition property

ΔAED ≅ ΔBEC                           Definition of congruency

≅                                   By CPCTC

The acronyms used in the proof are;

SAS: Side Angle Side rule of congruency

CPCTC: Congruent Parts of Congruent Triangles are Congruent

SSS: Side-Side-Side rule of congruency

Learn more about CPCTC here:

link

look in attachments

step-by-step explanation:

a = (-2, 0)

b= (-4, 0)

c = (-5,2)

d = (-1,2)

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