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mathematics

class VII

#### Key Concepts

congruent, SAS, RHS,SSS,ASA, congruence of triangles

#### essential questions

1.How do you show that two triangles are congruent?
2.How can you describe angles formed by parallel lines and transversals?
3. How can you describe the relationships among the angles of a triangle?
4. How can you find the sum of the interior angle measures and the sum of the exterior angle measures of a polygon?
5. How can you use angles to tell whether triangles are similar?

#### Remembering:

1. Which congruence criterion do we use in the following:  Given AC= AD , AB= DE , BC= EF So Δ ABC ≅ Δ DEF  a) SSS  b) ASA  c) SAS  d) RHS
2. Which congruence criterion do you use ∠B= ∠D=90°  a) SSS    b) RHS  c) ASA  d) SAS
3. If two line segments have the same ( equal) lenght, they are____ a) congruent  b) similar  c) opposite
4. Two angles are congruent if they have ____ a) equal measures  b) unequal measures  c) None
5. How many acute angles can a right angled triangle have: a) 1  b) 3  c) 3 d) None
6. Fill in the blanks:

a) Two line segments are congruent if they have___

b) Two angles are congruent if they have____

c) Two squares are congruent if they have____

d) Two circles are congruent if they have____

e) Two rectangles are congruent if they have____

f) Two triangles are congruent if they have___

#### understanding:

1. Which angle is included between the sides QR and PR  of Δ PQR: a) ∠ R  b)∠ Q  c) ∠ P  d) None
2. Δ ABC and Δ PQR are congruent under the correspondence. ABC↔ RQP. Write the parts of Δ ABC that corresponds to Δ PQR. a) AC  b) BC  c) None  d) AB
3. In congruent triangles ABC and DEF ∠ A= ∠ E= 40º and ∠ F= 65º , then find ∠ B a) None  b) 50º  c) 75º  d) 60º
4. Under a given correspondence, two triangles are congruent if the three sides of the one are equal to the three corresponding sides of the other. The above is known as: a) SSS congruence of two triangles  b) SAS congruence of two triangles c) ASA congruence of two triangles  d) RHS congruence of two triangles
5. Under a given correspondence, two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle. The above is known as: a) SSS congruence of two triangles  b) SAS congruence of two triangles c) ASA congruence of two triangles d) RHS congruence of two right angled triangles
6. Under a given correspondence, two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them of the the other triangle. The above is known as: a) SSS congruence of two triangles  b) SAS congruence of two triangles c) ASA congruence of two triangles  d) RHS congruence of two right angled triangle
7. The symbol of congruence is a)≡    b)≅  c)↔  d) =
8. The symbol of correspondence is  a)≡    b)≅  c)↔  d) =
9. If Δ ABC =Δ PQR then  line segment AB corresponds to: a) PQ  b) QR  c) RP  d) None
10. If Δ ABC =Δ PQR then line segment BC corresponds to a) PQ  b) QR  c) RP  d) None
11. If Δ ABC =Δ PQR then line segment CA corresponds to a) PQ  b) QR  c) RP  d) None
12. If Δ ABC =Δ PQR then line segment ∠A corresponds to a) ∠ P  b)∠ Q  c)∠ R  d) None
13. If  Δ ABC =Δ PQR then line segment ∠B corresponds to a) ∠ P  b)∠ Q  c)∠ R  d) None

#### Application:

1.  One of the acute angle of a right triangle is 36°, the other angle will be a) 54º   b) none  c) 64º  d) 34º
2. The hypotenuse of a right angled triangle is 37cm long. If one remaining two sides is 12 cm in length, then the length of the other side is: a) None  b) 35cm  c) 38cm  d) 30cm
3. In Δ ABC and Δ PQR, ∠ B=90º , AC= 8cm, AB= 3cm ∠P=90°, PR=3cm, QR=8cm. By which congruence rule the Δs are congruent?
4. We want to show Δ ART = Δ PEN and we have to use SSS criterion. We have AR= PE and RT= EN. What more do we need to show? a) AT= PN  b) AT= PE  c) AT=EN  d) None
5. We want to prove that Δ ART = Δ PEN, we have to use ASA criterion we have AT= PN, ∠A=∠P. What more do we need to show? a) ∠T= ∠N    b) ∠T= ∠E   c) ∠T= ∠P  d) None

#### Analysis:

1. Show that in an isosceles triangle, the angle opposite to the equal sides are equal.
2. Prove that the bisector of the vertical angle of an isosceles triangle bisects that base at right angle.

#### Evaluation:

1. If two triangles have their corresponding angles equal, are they always congruent? If not,, draw two triangles which are not congruent but which have their corresponding angles equal.
2. Are two triangles congruent if two sides and angle of one triangle are respectively equal to two sides and an angle of the other? If not then under what conditions will they be congruent?