Question

Show that ∆ABC=~ ∆PDC : a) Name the criteria used to prove congruence

b) If ACB =450 , What is the measure of CPD?​

Answer 1

Answer:

1. SSS (Side-side-side)

All three corresponding sides are congruent.

Eg: Consider △ABC and △PQR

PQ

AB

=

QR

BC

=

PR

AC

−

2

1

or AB=PQ,BC=QR,AC=PR

All the sides of triangle ABC are equal to all sides of △PQR

2. SAS [Side-angle-side]

Two sides and the angle between them are equal

In △ABC and △PQR,

AB=PQ;BC=QR,∠BAC=∠QPR

∴△ABC≅△PQR [by SAS Criteria]

3. AAS [angle-angle-side]

Two angles and a non- included sides are congruent.

Eg:

Consider the △ABC and △DEF,

BC∣∣EF and ∠ABC≅∠DEF .....(i)

∠BCA=∠EFD [corresponding angles of parallel lines are congruent].....(ii)

AD=CF

AD+CD=CF+CD [addition property of equality]

AC=AD+CD [partition postulate]

DF=CF+CD [partition postulate]

AC=DF [substitution property]....(iii)

From (i), (ii) and (iii),

△ABC≅△DEF [AAS Criteria]

4. ASA [angle-side-angle]

Two angles and the side between them are congruent.

Eg:

E is the mid-point of NO

∠SNW=∠TOA

Now, bisect ∠SNE and OA bisect ∠TOE ....(i)

As E is the midpoint, NE=EO.....(ii)

∠SEN≅∠TEO [vertical angles are congruent].....(iii)

From (i), (ii) and (iii),

△SNE≅△TOE [by ASA criteria]

i) SSS (side-side-side) = Option A

ii)SAS (side-angle-side) = Option D

iii)AAS (angle-angle-side) = Option C

iv) ASA (angle-side-angle) ) = Option B

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