Constructions of Triangles — Flashcards
Maharashtra Board · Class 9 · Mathematics
20 flashcards for Constructions of Triangles (Maharashtra Board Class 9 Mathematics) to test yourself on key terms and facts.
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What are the three new types of triangle constructions covered in this chapter?
Answer
1. Triangle with base, adjacent angle, and sum of remaining two sides 2. Triangle with base, adjacent angle, and difference of remaining two sides 3. Triangle with perimeter and two angles adjacent to…
State the Perpendicular Bisector Theorem.
Answer
1. Every point on the perpendicular bisector of a segment is equidistant from its end points. 2. Every point equidistant from the end points of a segment is on the perpendicular bisector of the segmen…
How many conditions are required to construct a triangle?
Answer
Three conditions are required to construct a triangle. Out of the three sides and three angles of a triangle, at least three independent pieces of information must be given to uniquely determine the t…
What property is frequently used in triangle constructions involving intersections?
Answer
If a point is on two different lines, then it is the intersection of the two lines. This property helps us locate specific points during construction by finding where two geometric conditions meet.
List the triangle constructions learned in previous standards.
Answer
1. Triangle when three sides are given (SSS) 2. Triangle when base and two adjacent angles are given (ASA) 3. Triangle when two sides and included angle are given (SAS) 4. Right-angled triangle when h…
In Construction I, what is the key insight for locating point A when given base BC, angle B, and AB + AC?
Answer
Since BD = AB + AC and A lies on ray BD, we have BA + AD = BA + AC, which means AD = AC. Therefore, point A lies on the perpendicular bisector of segment CD, and A is found at the intersection of ray …
What is Construction I used for?
Answer
Construction I is used to construct a triangle when its base, an angle adjacent to the base, and the sum of the lengths of the remaining two sides are given.
Step 1-3: How do you start Construction I for triangle ABC with BC = 6.3 cm, ∠B = 75°, and AB + AC = 9 cm?
Answer
Step 1: Draw segment BC of length 6.3 cm Step 2: Draw ray BP such that m∠PBC = 75° Step 3: Mark point D on ray BP such that d(B,D) = 9 cm…
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