Important points on Chapter
⇒Congruence of Triangles
⇒Practical geometry
Maths Class 7th
NCERT
At least 10 from each chapter .
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Answers
√ Here Is the answer You needed ^_^
✔ Congruence Of Triangle
→ In Geometry, When Two figures fit exactly on each other, we call them congruent figures or we say That They are in congruence.
✣ Congruent Triangles
→ Two Triangles are said to be congruent If they are exactly identical i.e If they are of the same shape and size.
→ Superposition : It is a method by placing one figure on to another so that we can establish Whether the given Figures are congruent or not.
→In two congruent Figures, the sides and angles are coincide By superposition are said to be correspond. They are also Called Corresponding sides and corresponding angles respectively.
→Symbol ≌ means "Is Congruent To"
✣ Conditions Of congruence of Triangles.
→ Side-Side-Side [ SSS] : In General, If The three sides of a Triangle are equal To the corresponding sides of another triangle, then the two Triangles are congruent.
→Side-Angle-Side [ SAS ] : If two triangles have corresponding sides equal and the angle is included between them is also equal, the two triangles are said to be congruent.
→Angle-Side-Angle OR Angle-Angle-Side [ ASA or AAS respectively ] : If Two triangles have one side equal and two corresponding angles equal, the two triangles are congruent.
→Right-Hypotenuse-Side [ RHS ] : If the Hypotenuse and one Side of a right angled triangle are equal to the hypotenuse and one of another right angled triangle, two triangles are congruent.
In the attachment, There's an example, Go through It!
✔ Practical Geometry
✣Rules for constructing a Parallel Line
→ If two lines are intersected by a transversal Line and if measures of any pair of corresponding are equal, then the lines are parallel.
→ If Two Lines are Intersected by a transversal, And If the measures of any Pair of alternate Interior angles are equal, The lines are parallel.
✣ Constructing Parallel lines using Set Squares and a Ruler.
Constructing a Parallel Line
⑴ Draw a Straight Line with the help of A ruler. Holding the Ruler fixed, Place a Set square along the ruler and Then Drag a straight Line. After that Slide That set square Along the Ruler so that It will maintain Some Distance from The previously Drawn Line. Then, Drag another Line through that set square.
✣ Constructing Parallel Lines using Ruler and Compass
⑴ Draw a Line Segment AB. Take Point P above it. Then, Take any point Q on AB and Join QP. At P, Draw ∠LPQ such that ∠LPQ = ∠BQP. After that, Extend LP to M to get line LM. LM is the required Line parallel to BA and passing through P.
✣ Construction of Triangle.
Advise : ⑴ To make a Rough Sketch Before Drawing the accurate figure.
⑵ Write the Given Data
⑶ Then Plan Construction of the figure according to the data given.
① To construct a Traingle when It's three sides are given.
example : Construct a triangle ABC in which AB = 3.5 cm, AC = 5cm and BC = 4 cm.
→ Steps of Construction.
Draw a Line segment AB = 3.5 cm.
With B as the Centre and radius 4 cm, draw an arc
With A as the Centre and Radius 5 cm, draw another arc cutting the first arc at point C
Join AC and BC
We Found ΔABC !
② To construct a Triangle when Two sides and the included angle is given.
example: Construct a Triangle ABC in which AB = 7cm, BC = 3cm, ∠B = 60°
→ Steps for construction
Draw a line segment AB = 7cm.
At B, draw an angle of 60° with the help of compass [ ∠ABX = 60° ]
with B as Centre and radius 3 cm, draw an arc cutting BX at C
Join AC,
Then, ABC is the required Triangle.
Like wise, You can draw many Triangles!
Sorry For the delay bachhi♡♡
Hope my answer will help you ♡
Answer:
Hey Nummu!
√ Here Is the answer You needed ^_^
✔ Congruence Of Triangle
→ In Geometry, When Two figures fit exactly on each other, we call them congruent figures or we say That They are in congruence.
✣ Congruent Triangles
→ Two Triangles are said to be congruent If they are exactly identical i.e If they are of the same shape and size.
→ Superposition : It is a method by placing one figure on to another so that we can establish Whether the given Figures are congruent or not.
→In two congruent Figures, the sides and angles are coincide By superposition are said to be correspond. They are also Called Corresponding sides and corresponding angles respectively.
→Symbol ≌ means "Is Congruent To"
✣ Conditions Of congruence of Triangles.
→ Side-Side-Side [ SSS] : In General, If The three sides of a Triangle are equal To the corresponding sides of another triangle, then the two Triangles are congruent.
→Side-Angle-Side [ SAS ] : If two triangles have corresponding sides equal and the angle is included between them is also equal, the two triangles are said to be congruent.
→Angle-Side-Angle OR Angle-Angle-Side [ ASA or AAS respectively ] : If Two triangles have one side equal and two corresponding angles equal, the two triangles are congruent.
→Right-Hypotenuse-Side [ RHS ] : If the Hypotenuse and one Side of a right angled triangle are equal to the hypotenuse and one of another right angled triangle, two triangles are congruent.
In the attachment, There's an example, Go through It!
✔ Practical Geometry
✣Rules for constructing a Parallel Line
→ If two lines are intersected by a transversal Line and if measures of any pair of corresponding are equal, then the lines are parallel.
→ If Two Lines are Intersected by a transversal, And If the measures of any Pair of alternate Interior angles are equal, The lines are parallel.
✣ Constructing Parallel lines using Set Squares and a Ruler.
Constructing a Parallel Line
⑴ Draw a Straight Line with the help of A ruler. Holding the Ruler fixed, Place a Set square along the ruler and Then Drag a straight Line. After that Slide That set square Along the Ruler so that It will maintain Some Distance from The previously Drawn Line. Then, Drag another Line through that set square.
✣ Constructing Parallel Lines using Ruler and Compass
⑴ Draw a Line Segment AB. Take Point P above it. Then, Take any point Q on AB and Join QP. At P, Draw ∠LPQ such that ∠LPQ = ∠BQP. After that, Extend LP to M to get line LM. LM is the required Line parallel to BA and passing through P.
✣ Construction of Triangle.
Advise : ⑴ To make a Rough Sketch Before Drawing the accurate figure.
⑵ Write the Given Data
⑶ Then Plan Construction of the figure according to the data given.
① To construct a Traingle when It's three sides are given.
example : Construct a triangle ABC in which AB = 3.5 cm, AC = 5cm and BC = 4 cm.
→ Steps of Construction.
Draw a Line segment AB = 3.5 cm.
With B as the Centre and radius 4 cm, draw an arc
With A as the Centre and Radius 5 cm, draw another arc cutting the first arc at point C
Join AC and BC
We Found ΔABC !
② To construct a Triangle when Two sides and the included angle is given.
example: Construct a Triangle ABC in which AB = 7cm, BC = 3cm, ∠B = 60°
→ Steps for construction
Draw a line segment AB = 7cm.
At B, draw an angle of 60° with the help of compass [ ∠ABX = 60° ]
with B as Centre and radius 3 cm, draw an arc cutting BX at C
Join AC,
Then, ABC is the required Triangle.
Like wise, You can draw many Triangles!
Hope my answer will help you ♡