Geometrical Constructions — Flashcards
Telangana Board · Class 9 · Mathematics
20 flashcards for Geometrical Constructions (Telangana Board Class 9 Mathematics) to test yourself on key terms and facts.
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Construct the perpendicular bisector of line segment AB = 6 cm using ruler and compass only. List the steps.
Answer
Step 1: Draw line segment AB = 6 cm. Step 2: Take A as center, draw arc with radius > 3 cm on both sides of AB. Step 3: Take B as center with same radius, draw arcs intersecting previous arcs at P and…
Prove that in perpendicular bisector construction, the line PQ actually bisects AB perpendicularly.
Answer
Proof: In triangles PAQ and PBQ: AP = BP (equal radii), AQ = BQ (equal radii), PQ = PQ (common). Therefore △PAQ ≅ △PBQ (SSS rule). So ∠APO = ∠BPO (CPCT). In △APO and △BPO: AP = BP, ∠APO = ∠BPO, OP = O…
Construct an angle of 60° at point A on ray AB using compass and ruler. Show all steps.
Answer
Step 1: Draw ray AB with initial point A. Step 2: Take A as center with any radius, draw arc intersecting AB at D. Step 3: Take D as center with same radius, draw arc intersecting previous arc at E. S…
How do you construct a 30° angle using the 60° angle construction?
Answer
Step 1: First construct 60° angle using standard method. Step 2: Bisect the 60° angle. Method: Take any radius from vertex, mark arcs on both rays. From these points, draw equal arcs intersecting insi…
Construct triangle ABC with BC = 5 cm, ∠B = 60°, and AB + AC = 8 cm. Show construction steps.
Answer
Step 1: Draw BC = 5 cm. Step 2: At B, construct ∠CBX = 60°. Step 3: From B on ray BX, mark point D such that BD = 8 cm. Step 4: Join CD. Step 5: Draw perpendicular bisector of CD meeting BD at A. Step…
Why does the construction AB + AC = BD work in the previous triangle construction?
Answer
Conceptual explanation: When we mark D on BX such that BD = AB + AC, and draw perpendicular bisector of CD, point A lies equidistant from C and D. Therefore AC = AD. Since A lies on BD, we have BD = B…
Construct triangle PQR with QR = 6 cm, ∠Q = 45°, and PQ - PR = 2 cm (where PQ > PR).
Answer
Step 1: Draw QR = 6 cm. Step 2: At Q, construct ∠RQX = 45°. Step 3: On QX, mark point S such that QS = 2 cm (= PQ - PR). Step 4: Join RS. Step 5: Draw perpendicular bisector of RS meeting QX at P. Ste…
When should you use case (i) vs case (ii) for difference of sides construction?
Answer
Case (i): When AB > AC, use AB - AC. Mark point D on AB extended such that BD = AB - AC. Case (ii): When AB < AC, use AC - AB. Mark point D on AB produced such that BD = AC - AB. Key difference: In ca…
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