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

third option: 6x+8

step-by-step explanation:

we can see that the given question is a sum of series and the values of n vary from 0 to 3

the first term will be:

when n=0, [(0)*x+2] => (0+2) => 2

when n=1, [(1)*x+2] => (x+2) => x+2

when n=2, [(2)*x+2] => 2x+2

when n=4, [(3)*x+2] => 3x+2

so adding up all the terms will give us:

=2+x+2+2x+2+3x+2

=x+2x+3x+2+2+2+2

=6x+8

so,

third option is the correct answer ..

where are the options?

step-by-step explanation: