Page 53 - CT&AI_CLasa_7_Part_1

6. If the angles of a triangle are in the ratio 1 : 2 : 7, the entire set is composed of only three
then the triangle is a/an . distinct geometric species. To prove this, you
(Analytical Thinking) must analyse the properties of the pieces
(angles and side relationships).If you were
(a) Acute-angled triangle to categorize these 7 pieces based on their
geometric shape name (regardless of their
(b) Obtuse-angled triangle
size), which of the following represents the
(c) Right-angled triangle correct classification of the set?
(Pattern Recognition)
(d) Right-angled isosceles triangle
(a) The Trio: 5 Isosceles Right Triangles,
7. You have discovered a digital vault protected 1 Square, and 1 Parallelogram.
computational thinking quest by a “Symmetry Key.” The key is a perfect
6-pointed star (a Hexagram) formed by two (b) The Spectrum: 7 Unique shapes
overlapping, congruent equilateral triangles that cannot be mapped to one
Tick ( ) the correct option. centered on the same point. To unlock the another.
vault, you must rotate the star until it perfectly (c) The Binary: 6 Triangles and 1
aligns with its original “resting state.” However, Quadrilateral.
the vault’s computer is programmed to be
efficient: it only accepts the smallest positive (d) The Scale: 5 Triangles of different
rotation that results in an identical visual angles, 1 Rhombus, and 1
configuration. Rectangle.
What is the rotational symmetry of this 10. For the “Eyes” construction, A
created star (Hexagram)? (Critical Thinking) as shown adjacent if points
A and B are the centers for
(a) 30° (b) 60° the upper and lower arcs X Y
for the EYE, what must B
(c) 90° (d) 120° be true for the EYE to be
7. If you place four equilateral triangles around a symmetrical?
single point, what is the “gap angle” remaining (Logical Thinking)
to complete the 360°? (Abstract Thinking)
(a) AX = AY and BX = BY
(a) 30° (b) 60°

(b) AX = BX and AY = BY
(c) 90° (d) 120°
9. You are given a standard 7-piece Tangram (c) AX = AY = BX = BY
set. A master designer claims that although
there are 7 physical pieces, the “DNA” of (d) AB = XY

An 8 × 8 chessboard has two squares of the same colour removed (the top-left
and bottom-right corners, both white). You have 31 dominoes, each covering
exactly two squares (2 × 1). Is it possible to tile the remaining 62 squares
perfectly?

(a) No, the grid is no longer a perfect square.

(b) Yes, we can place the tiles diagonally.

(c) No, because every domino must cover one white one black square.

(d) Yes, because 62 is an even number.

Construction and Tilings 51