Exercise – 10.1-class seven

Read More »## Exercise 10.1|Class seven| Congruence| Part – 2

Problem – 5: In the figure, AD = AE, BD = CE and ∠AEC = ∠ADB. Prove that AB = AC. Particular enunciation: In the figure, AD = AE, BD = CE and ∠AEC = ∠ADB. We have to prove that AB = AC. Proof: In ∆ACE and ∆ADB, AD ...

Read More »## Solution exercise 9.1| Class seven| Geometry

Problem-1: In the figure, ∆ABC is a triangle in which ∠ABC = 900, ∠BAC =480 and BD is perpendicular to AC. Find the remaining angles. Solution: Let remaining angles ∠ABD = x, ∠DBC = y and ∠BCD = z. Since BD⊥AC ∴ ∠ADB = ∠CDB = 900 Now, in ∆ABD ...

Read More »## Exercise 10.1|Class seven| Congruence| Part – 1

Problem – 1: In the figure, CD is the perpendicular bisector of AB, Prove that ∆ADC ≅ ∆BDC. Solution: Particular enunciation: Given that, in the figure, CD is the perpendicular bisector of AB. i.e., AD = BD. We have to prove that, ∆ADC ≅ ∆BDC. Proof: In ∆ADC and ∆BDC, ...

Read More »## If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.

If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects. Particular enunciation: In the ∆ABC and ∆DEF, AB = DE, AC = DF and BC = EF, We have to proved ...

Read More »## If two angles of triangles are equal, then the sides opposite to the equal angles are equal.

If two angles of triangles are equal, then the sides opposite to the equal angles are equal. Particular enunciation: Let ABC be a triangle in which the ∠ACB = the ∠ABC. We have to prove that AB =AC. Proof: If AC and AB are equal, suppose that AB>AC. From BA ...

Read More »## Solution of exercise 9.2(Triangle)| Class seven

Problem-9: In the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. Prove that PB>PC. Particular enunciation: Given that, in the triangle ABC, AB>AC and the bisectors of the ∠B and ∠C intersect at the point P. We have to prove that PB>PC. ...

Read More »## If two sides of a triangle are equal, then the angles opposite the equal sides are also equal

General enunciation: If two triangles have two sides of the one equal to two sides of the other, each to each, the angles included by those sides are also equal then the triangles are equal in all respect. Particular Enunciation: Let, ∆ABC and ∆DEF be two triangles in which AB=DE, ...

Read More »## If three sides of a triangle are respectively equal to the corresponding three sides of another triangle, then the triangle are congruent.

General enunciation: If three sides of a triangle are respectively equal to the corresponding three sides of another triangle, then the triangle are congruent. Particular enunciation: Let, in ∆ABC and ∆DEF, AB = PQ, AC = PR and BC = QR. It is required to prove that, ∆ABC ≌ ...

Read More »## The straight lines which are parallel to the same straight line are parallel to one another.

Theorem: If a straight line intersects another two straight lines and if the corresponding angles are equal to each other. General enunciation: If a straight line intersects another two straight lines and if the corresponding angles are equal to each other. Particular enunciation: Let the straight line PQ intersects AB ...

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