Lines and Angles
In ΔABC, ∠ABC = 60° and ∠BCA = 50°. Find ∠CAB.
∠CAB = 70° (Sum of angles in a triangle is 180°).
In ΔPQR, PQ = PR and ∠P = 40°. Find ∠Q and ∠R.
∠Q = ∠R = 70° (Base angles of an isosceles triangle are equal).
Are the opposite angles of a parallelogram are equal?
yes
Reason that the angle subtended by a diameter at the circumference is 90°.
semicircle theorem
If AB is parallel to CD and ∠1 = 72°, find ∠2.
∠2 = 72° (Corresponding angles are equal).
Prove that the sum of the lengths of two sides of a triangle is greater than the third side.
Triangle inequality theorem: Any two sides' sum is greater than the third side.
In a rhombus, one angle is 60°. Find the other angles.
60°, 120°, 120°, 60° (Opposite angles are equal, adjacent angles are supplementary).
If two chords of a circle are equal, what can you say about their corresponding arcs?
Their arcs are equal.
Two lines intersect such that one angle is 110°. Find its vertically opposite angle.
110° (Vertically opposite angles are equal)
A right-angled triangle has a hypotenuse of 10 cm and one side of 6 cm. Find the other side.
8 cm (Using Pythagoras' theorem: 10^2=6^2+x^2
Are the diagonals of a rectangle are equal.
.
yes
What ca be used to prove that the opposite angles of a cyclic quadrilateral are supplementary.
Use the properties of angles subtended by the same arc.
A triangle has angles in the ratio 2:3:4. Find the size of the smallest angle.
40° (2x + 3x + 4x = 180°).
state the midpoint theorem
The line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.
What can we use to show that the diagonals of a parallelogram bisect each other.
Using congruence between the triangles formed.
A chord is 8 cm away from the center of a circle with a radius of 10 cm. Find the chord length.
12 cm (Using Pythagoras' theorem
If ∠PQR = 90° and PS is a perpendicular from P to QR, what is the measure of ∠SPR?
90° (Angle between a perpendicular line and the base).
In ΔABC and ΔDEF, ∠A = ∠D, ∠B = ∠E, and AB/DE = AC/DF. Are the triangles similar?
Yes, by the SAS similarity criterion
A square has a side length of 6 cm. Find the length of its diagonal.
72\sqrt{72}72 or 626\sqrt{2}62 cm (Using Pythagoras: d^2 = 6^2 + 6^2
What can be used to prove that tangents drawn from an external point are equal in length.
Use congruent triangles formed by radii and tangents.