Math, asked by singhsurjit2530, 5 months ago

can I use ASA congurence rule and conclude that triangle AOC=_traingle BOD ​

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Answers

Answered by vanshikaa740
1

Answer:

yes because if you can see angle c A b is equals to angle a BD because AC and BD is parallel to each other so angle c A b will be equal to angle a BD by alternate interior angle property and ac is also equals to BD as they as it is given so you can write it by asa also but more relevant answer should be aas

Answered by Agamsain
60

Answer :-

  • 'No' We can't use ASA congruence rule to show that ΔAOC ≅ ΔBOD
  • We can use AAS congruence rule to show that ΔAOC ≅ ΔBOD

Reason :-

  • The Reason behind this is that both triangles are unable to fulfill the requirements of the ASA Congruence Rule.

Given :-

  • ∠AOC = ∠BOD = 30°
  • ∠ACO = ∠BDO = 70°
  • AC = BD = 3 cm

To Show OR To Prove :-

  • Can we ASA congruence rule to show that ΔAOC ≅ ΔBOD ?

Explanation :-

In Order to get the answer, First we need to understand two congruence rule,

  • ASA (Angle Side Angle) :- If any two angles and side included between the angles of one triangle are equivalent to the corresponding two angles and side included between the angles of the second triangle, then the two triangles are said to be congruent by ASA rule.

  • AAS (Angle Angle Side) :- When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

We can't use ASA Congruence rule because In the Given figure the 2 Triangles Failed to fulfill the property of ASA Rule.

AC is not included in the angles ∠ACO and ∠AOC

                                      And

BD is not included in the angles ∠BDO and ∠BOD

➠ In ΔAOC and ΔBOD,

\rm \implies \angle AOC = \angle BOD \qquad \bold{[Vertically \; Opposite \; Angle]}

\rm \implies \angle ACO = \angle BDO \qquad \bold{[Given]}

\rm \implies AC = BD \qquad \quad \; \; \; \; \; \; \; \; \bold{[Given]}

\rm Hence, \triangle AOC \cong \triangle BOD \; By \; \bold {AAS \: Congruence \: Rule}

With Regards,

@Agamsain

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