Congruence of Triangles | Chapter Assessment | English | Grade 7

Sumit has drawn 2 line segments. So in which case they will be congruent?

• They should be parallel

• They should have different lengths

• They should have equal lengths

• Both option 1 and option 3

Answer explanation

When two line segments are of equal lengths then they are congruent. Hence option 3 is the right answer.

Tags

CCSS.8.G.A.2

Which one of the following statements is true?

• If three angles of a triangle are equal to three angles of another triangle, then both the triangles are congruent

• If two angles and any one side of a triangle are equal to two angles and any one side of another triangle, then both the triangles are congruent

• If two sides and any one angle of a triangle are equal to two sides and any one angle of another triangle, then both the triangles are congruent

• If the hypotenuse and one leg of a right-angled triangle are equal to the hypotenuse and one leg of another right-angled triangle, then both the triangles are congruent.

Answer explanation

We know that, if the three angles of one triangle are equal to the three angles of the another triangle then the triangles may or may not be congruent. Because in this case the length of sides of the triangles may vary. So statement of option 1 is false. If two angles and any one side of a triangle are equal to the two angles and any one side of the another triangle then the triangles may or may not be congruent. Since for congruence the side that is included between the two angles must be equal. So statement of option 2 is false. Similarly, two triangles are congruent if two sides and the angle included between the sides is equal to the corresponding two sides and the angle included between the sides of another triangle. In the statement of option 3 the included word is missing. Hence this is also the false statement. When the length of the hypotenuse and one leg of a right-angled triangle are equal to the hypotenuse and one leg of another right-angled triangle then the triangles are congruent under RHS criterion. Hence the statement of option 4 is true.

Tags

CCSS.HSG.SRT.B.5

Which one of the following is not a criterion for congruence of two triangles?

• SAS

• ASA

• SSA

• SSS

Answer explanation

SSA is not a criterion for the congruence of two triangles.

Tags

CCSS.HSG.SRT.B.5

In the following figure, LC is the bisector of ∠L and side LU = side LK. Then △LUC and △LKC are congruent by the criterion:

• ASA

• AAA

• SAS

• Both option 1 and option 3

Answer explanation

In the given figure, LC is the bisector of ∠L Therefore ∠CLU = ∠CLK Now in △LUC and △LKC side LU = side LK .....(given) SIde LC = side LC .....(common) and ∠CLU = ∠CLK .....(since LC is the bisector) In △LUC, ∠CLU is included between the sides LU and LC. Similarly in △LCK, ∠CLK is included between the sides LC and LK. So △LUC ≅ △LKC by SAS congruence criterion. We not know the measure of ∠U and ∠K so we can not say that △LUC ≅ △LKC by ASA congruence criterion. Hence option 3 is the right answer.

Tags

CCSS.HSG.SRT.B.5

The two triangles in the following figure are congruent by which congruency criterion?

• SSS

• SAS

• ASA

• Both option 1 and option 2

Answer explanation

In the given figure we can see that in △SOM and △SOE, Side SM = side SE ....(given) Side MO = side EO .....(given) Side SO = side SO ......(Common) We know that when the lengths of three sides of a triangle are equal to the corresponding lengths of the three sides of another triangle, then the triangles are congruent under SSS criterion. Therefore △SOM ≅ △SOE by SSS congruency criterion. Hence option 1 is the right answer.

Tags

CCSS.HSG.SRT.B.5

In the following figure, △GOT ≅ △NOW by ASA congruence criterion. Then what will be the value of y?

• 90⁰

• 80⁰

• 60⁰

• 40⁰

Answer explanation

In figure we can see that in △GOT, ∠O = 40⁰ and ∠T = 60⁰ It is given that △GOT ≅ △NOW by ASA congruence criteria. So G ↔ N, O ↔ O and T ↔ W Since corresponding parts of congruent triangle are equal. Therefore ∠G = ∠N, ∠O = ∠O and ∠T = ∠W That is ∠O = ∠O = 40⁰ and ∠T = ∠W = 60⁰. We know that according to angle sum property of triangles the sum of all three interior angles of a triangle is 180⁰ Therefore in △NOW, ∠N + ∠O + ∠W = 180⁰ ∠N + 40⁰ + 60⁰ = 180⁰ ∠N + 100⁰ = 180⁰ ∠N = 180⁰ - 100⁰ = 80⁰ So ∠N = y = 80⁰ Therefore the value of y is 80⁰.

Tags

CCSS.HSG.CO.B.7

If △ABC is congruent to △DEF by SAS congruence criterion, then what is the value of x?

• 25⁰

• 60⁰

• 75⁰

• 15⁰

Answer explanation

In figure we can see that in △ABC and △DEF, side AB = side DE, side BC = side EF, ∠B = 5x - 30⁰ and ∠E = 2x + 15⁰. △ABC ≅ △DEF, So A ↔ D, B ↔ E and C ↔ F Since corresponding parts of congruent triangles are equal therefore ∠A = ∠D, ∠B = ∠E and ∠C = ∠F That is 5x - 60⁰ = 2x + 15⁰ 5x - 2x = 60⁰ + 15⁰ 3x = 75⁰ x = 75⁰/3 = 25⁰ Hence the value of x is 25⁰ and option 1 is the right answer.

Tags

CCSS.HSG.CO.B.7

In △EFG, line segment GH is perpendicular to side EF, line segment FI is perpendicular to side EG and GH = FI. Then what will be the length of GH?

• 100 cm

• 10 cm

• 8 cm

• 6 cm

Answer explanation

In △EFG, line segment GH is perpendicular on side EF, line segment FI is perpendicular on side EG. Therefore △HFG and △IGF are right-angled triangle. So GH is hypotenuse of △HFG and FI is hypotenuse of △IGF In △HFG and △IGF, Hypotenuse GH = hypotenuse FI .....(given) Side FG = side FG ......(common) When the hypotenuse and one leg of a right-angled triangle is equal to the hypotenuse and one leg of another right-angled triangle then the triangles are congruent under RHS criteria. Therefore △HFG ≅ △IGF by RHS congruence criteria. Since the congruent parts of congruent triangle are equal therefore In △HFG and △IGF side FG = side FG = 8 cm side IG = side FH = 6 cm By Pythagoras property of right-angled triangles, (Hypotenuse)² = Sum of squares of legs Therefore HG² = FG² + FH² HG² = (8 cm)² + (6 cm)² HG² = 64 cm² + 36 cm² HG² = 100 cm² HG² = √100 cm² = 10 cm Hence option 2 is the right answer.

Tags

CCSS.HSG.CO.C.9