Unit 4 Test Congruent Triangles

Test FOR CONGRUENCE OF TRIANGLES

Two triangles are coinciding if they are identical except for position.

Simply, If one triangle was cutting with scissors and placed on the top of the other, they would friction match each other perfectly.

The higher up triangles are congruent.

We writeΔABC≅ΔXYZ

where≅ reads "is congruent to".

Exam for Congruence triangles

Two triangles are coinciding if one of the following is true :

All corresponding sides are equal in length (SSS)

SSS

Two sides and the included angle are equal (SAS)

SAS

Ii angles and a pair of corresponding sides are equal.

For right angled triangles, the hypotenuses and ane pair of sides are equal (RHS)

RHS

Are the following pairs of triangles are congruent ? If so, state the congruence relationship and give a cursory reason.

Example 1 :

Solution :

In the given ∆PQR and ∆XYZ,

PR = ZX (Southwardides)

∠ PRQ = ∠ ZXY ( A ngles)

RQ = XY ( S ides)

And then, ∆PRQ ≅ ∆ZXY

Using SAS congruence Postulate

Instance 2 :

Solution :

In the given ∆ABC and ∆KLM,

AB = KL ( South ides)

AC = LM ( South ides)

BC = KM ( S ides)

Then, ∆ABC ≅ ∆KLM

Using SSS congruence Postulate

Example three :

Solution :

In the given ∆ABC and ∆FED,

∠ C = ∠ D ( A ngles)

∠ A = ∠ F ( A ngles)

BC = ED ( S ides)

BC and ED are corresponding sides contrary to ten.

And then, ∆ABC ≅ ∆FED

Using AAcorS congruence Postulate

Example four :

Solution :

In the given ∆ABC and ∆EDF,

∠ B = ∠ D ( A ngles)

∠ C = ∠ F ( A ngles)

AB = ED ( S ides are corresponding to the angles)

So, ∆ABC ≅ ∆EFD

Using AAcorS congruence postulate

Example 5 :

Solution :

In the given ∆ABC and ∆FED,

∠ B = ∠ E ( A ngles)

∠DEF +∠EDF +∠EFD = 180 °

90 ° + xxx ° + ∠ EFD = 180 °

∠ EFD = 180 ° - 120 °

∠ EFD = 60 °

∠ A = ∠ F ( A ngles)

BC = ED ( S ides)

which is reverse to the angles ∠ A = ∠ F

So, ∆ABC ≅ ∆EFD

Using AAcorS congruence Postulate

Example half-dozen :

Solution :

In the given ∆PQR and ∆FED,

Hither the only one pair of angles and sides are the same, and so it'southward not congruent triangles.

So, ∆PQR ≇ ∆FED

Example 7 :

Solution :

In the given ∆ABC and ∆PQR,

AB = PR ( South ides)

AC = PQ ( Due south ides)

BC = RQ ( S ides)

And so, ∆ABC ≅ ∆PQR

Using SSS congruence postulate

Instance 8 :

Solution :

In the given ∆ABC and ∆XYZ.

Here all the angles are equal, then triangles are too similar but not coinciding triangles.

And so, ∆ABC ≇ ∆XYZ

Instance 9 :

Solution :

In the given ∆ABC and ∆EFD

∠ D = ∠ B = α (Angles)

∠ E = ∠ C = β (Angles)

Only EF and BC are non equal to corresponding sides.

And then, ∆ABC ≇ ∆EFD

Instance ten :

Solution :

In the given ∆DEF and ∆ZYX.

∠ E = ∠ Y ( R ight Angles)

FD = ZX ( H ypotenuse sides)

EF = YX ( South ides)

And then, ∆DEF ≅ ∆ZYX

Using RHS congruence postulate

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