Cyclic quadrilateral ABCD satisfies ∠ABD = 70◦ , ∠ADB = 50◦ , and BC = CD. Suppose AB intersects CD at point P, while AD intersects BC at point Q. Compute ∠AP Q − ∠AQP
Answers
Answer:
Angle Chasing and Similarity
JV Practice
C.J. Argue
1 Techniques
1. Complementary, supplementary angles.
2. Vertical angles.
3. Angles from parallel lines.
4. Sum of angles in a triangle, general polygon.
5. Isoceles triangle.
2 Warm-Up Problems
1. Show that the sum of the angles of a triangle is 180◦
.
2. (David Altizio) Suppose ABCD is a convex quadrilateral with ∠ABC = 144◦
, ∠ADC = 105◦
,
and AB = BD = DC. Compute ∠BCD − ∠BAD.
3. (AHSME 1960) In the diagram below AB and AC are the equal sides of an isosceles 4ABC,
in which is inscribed equilateral 4DEF. Designate ∠BF D by a, ∠ADE by b, and ∠F EC
by c. Which of the following is true?
(A) b =
a+c
2
(B) b =
a−c
2
(C) a =
b−c
2
(D) a =
b+c
2
(E) none of these
3 Problems
1. Find a formula for the sum of the angles of a polygon with n sides. (You may know the
formula, but can you prove it?) Does this formula hold for concave polygons?
1
Western PA ARML Geometry 1 1/13/2019
Step-by-step explanation: