Maths 5 marks

Here CA and DB are perpendicular to AB.
Yes CA and DB are parallel.

Construction:
(i) Drawn a line segment AB of length 6 cm.
(ii) Place the set square on the line in such a way that the vertex of its right angle coincides with B first and A next and one arm of the right angle coincides with the line AB.
(iii) Drawn lines DB and CA through B and A, the other arm of the right angle of the set square.
(iv) The line CA and DB are perpendicular to AB at A and B.

(a) BC = 1 + 1 + 1 + 1 = 4 cm
AB = AC = 4 cm
∆ABC is an equilateral triangle.
(b) ∆ABC and ∆AEF are isosceles triangles.
Since AB = AC = 4 cm
Also AE = AF.
(c) In a scalene triangle, no two sides are equal.
∆AEB, ∆AED, ∆ADF, ∆AFC, ∆ABD, ∆ADC, ∆ABF and ∆AEC are scalene triangles.
(d) In an acute-angled triangle all the three angles are less than 90°
∆ABC, ∆AEF, ∆ABF and ∆AEC are acute-angled triangles.
(e) In an obtuse-angled triangle any one of the angles is greater than 90°
∆AEB and ∆AFC are obtuse angled triangles.
(f) In a right triangle, one of the angles is 90°
∆ADB, ∆ADC, ∆ADE and ∆ADF are right-angled triangles.

Step 1: Using a scale draw a line AB and mark a point Q on the line.
Step 2: Place the set square in such a way that the vertex of the right angle coincides with Q and one of the edges of right angle lies along AB.
Mark the point R such that QR = 5.4 cm
Step 3: Place the scale and the set square as shown in the figure.
Step 4: Hold the scale firmly and slide the set square along the edge of the scale until the other edge touches the point R.
Draw a line RS through R.
Step 5: The line RS is parallel to AB. That is, RS || AB.figure.
Step 4: Hold the scale firmly and slide the set square along the edge of the scale until the other edge touches the point R.
Draw a line RS through R.
Step 5: The line RS is parallel to AB.

Step 1: Draw a line. Mark two points M and N on the line such that MN = 7.8 cm.
Mark a point B any where above the line.
Step 2: Place the set square below B in such a way that one of the edges that form a right angle lies along MN Place the scale along the other edge of the set square.
Step 3: Holding the scale firmly, Slide the set square along the edge of the scale until the other edge of the set square reaches the point B.
Through B draw a line.
Step 4: The line MN is parallel to AB.
That is, MN || AB.

Making the points P, Q, R, S and A, B, C, D on the given lines
PQ = RS = 0.9 cm
AB = CD = 1 cm
Distance between the two lines are equal.
They are parallel lines.

Step 1: Draw a line LM = 6.5 cm and take a point X anywhere above the line LM.
Step 2: Place one of the arms of the right angle of a set square along with the line LM and the other arm of its right angle touches the point X.
Step 3: Draw a line through the point X meeting LM at Y.
Step 4: The line XY is perpendicular to the line LM at Y.
That is, LM ⊥ XY.

Step 1: Draw a line AB = 7 cm and take a point P anywhere on the line.
Step 2: Place the set square on the line in such a way that the vertex which forms right angle coincides with P and one arm of the right angle coincides with the line AB.
Step 3: Draw a line PQ through P along the other arm of the right angle of the set square.
Step 4: The line PQ is perpendicular to the line AB at P.
That is, PQ ⊥ AB
∠APQ = ∠BPQ = 90°