ASA Congruence Criterion | Congruence of Triangles | Assessment | English | Grade 7

If under a given correspondence, two angles and the included side of a triangle are equal to two corresponding angles and the included side of another triangle, then the triangles are congruent. This is known as

• RHS congruence criterion

• ASA congruence criterion

• SSS congruence criterion

• SAS congruence criterion

Answer explanation

When two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle then the triangles are congruent under ASA criterion. Therefore, when two triangles are congruent under ASA criterion then their two angles and the included side are equal. Hence option 4 is the right answer.

Tags

CCSS.HSG.SRT.B.5

Which of the following pairs of triangles is congruent under ASA congruence criterion?

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Answer explanation

When two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle then the triangles are congruent under ASA criterion. Here in option 1, in △ABC two angles ∠B and ∠C and the side BC included between them are equal to the two angles ∠Q and ∠R and the side QR included between them of △PQR. Therefore △ABC ≅ △PQR Hence option 1 is the right answer.

Tags

CCSS.HSG.SRT.B.5

By which of the following criterion two triangles cannot be proved congruent?

• SAS

• AAA

• ASA

• None of the above

Answer explanation

Two triangles can be proved congruent by SSS criterion, SAS criterion and ASA criterion. Two triangles cannot be proved as congruent by AAA criterion For example, the measures of all three interior angles of △ABC are equal to the measures of all three corresponding interior angles of △PQR, but △ABC ≇ △PQR as the side lengths are not equal. Hence option 2 is the correct answer.

Tags

CCSS.8.G.A.2

In △XYZ and △KLM, ∠X = ∠K and ∠Y = ∠L. Then what additional information is needed to establish congruence by ASA criterion?

• side XY = side KL

• side XY = side KM

• side XZ = side KL

• None of the above

Answer explanation

In △XYZ and △KLM, ∠X = ∠K and ∠Y = ∠L When two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle then the triangles are congruent under ASA criterion. Here in △XYZ side included between ∠X and ∠Y is XY and in △KLM side included between ∠K and ∠L is KL. So △XYZ will be congruent to △KLM when side XY = side KL Hence additional information needed to establish congruence by ASA criterion is side XY = side KL Hence option 1 is the right answer.

Tags

CCSS.HSG.SRT.B.5

In the following figure, ∠1 = ∠2 and ∠3 = ∠4. Then which of the following Option is true?

• Side XW = side YW

• Side XW = side XY

• Side XW = side XZ

• Side XW = side YZ

Answer explanation

In the figure, ∠1 = ∠2 and ∠3 = ∠4 is given. We can see that side XY is common in both triangles △WXY and △ZXY. In △WXY, the side XY is included between ∠1 and ∠3 Similarly in △ZXY, the side XY is included between ∠2 and ∠4 So we can say that △WXY ≅ △ZXY by ASA criterion. We know that the corresponding parts of congruent triangles are equal therefore Side XW = side XZ. Hence Option 3 is true.

Tags

CCSS.HSG.CO.C.11

Somya has drawn the following figure in which AB || CD and AB = CD. Then which of the following statement is right?

• △ABO ≅ △COD

• △OAB ≅ △OCD

• △ABO ≅ △CDO

• None of the above

Answer explanation

In the figure AB∥CD and AB = CD We can see that BC is the transversal of AB and CD So ∠2 and ∠4 are the alternate interior angles. We know that when transversal intersects two parallel lines then each pair of alternate interior angle is equal. Therefore ∠2 = ∠4 Similarly AD is also the transversal of AB and CD So ∠1 and ∠3 are the alternate interior angles. Therefore ∠1 = ∠3 Now in △OAB, side AB is included between ∠1 and ∠2. Similarly in △ODC, side CD is included between ∠3 and ∠4. So by ASA congruence criterion, △OAB ≅ △ODC In which O↔ O, A↔ D and B↔ C Hence under this correspondence △ABO ≅ △DCO So △ABO ≇ △COD, △OAB ≇ △OCD and △ABO ≇ △CDO Therefore option 4 is the right answer.

Tags

CCSS.HSG.CO.B.7