Solution:
In triangle ABC
AC=3
AB=4
BC=5
In triangle BDE
BD=2 (D is the midpoint of AB )
In both triangle are similar
A 5. GIVEN: AABC is isosceles D is the midpoint of BC FDI AC DE 1 AB PROVE: FD - DE F E С B
4. The following figure shows triangle AABC with side lengths AB = 10, BC = 8, and CA = 5. DE is constructed to be parallel to AB and to originate at point D, the midpoint of AC. C X10 D Ε B A Write the lengths for the segments listed below. BE = ED= DA=
3 nat you ho has cheated on this exam. 1. Let AABN and AA'B'Y by asymptotic triangles. Prove that if LABN 2 ZA'B'Y and AB> ΑΒ , then /BAΩ< ΒA. 2. Let AABC be an ordinary triangle and let D be any point of the interior. Prove that the sum of the angles of AABD is greater than the sum of the angles of AABC. 3. Suppose that two lines & and m have a common perpendicular MN. Let A...
Additional Problem: Suppose that AABC has sides AB 31,AC 35, and M is the midpoint of BC. The goal is to obtain the inequality 2 < x <33, where x AM. Construct the auxiliary lines shown, with M the midpoint of AE a. Find y-CE. Then show that 2x-AE 66. b. Show that AM (66)-33 C. Show that 2 < x < 33. (Hint: Use the Triangle Inequality in AEC. 31 35
Kindly answer the question neatly. Thanks. In AABC, AB = AC and BC = 6 cm. D is a point on the side AC such that AD = 5 cm and CD = 4 cm. Show that ABCD – AACB and hence find BD.
the vertices of AABC lie on a circle and AB is a diameter of thar circle, then ZACB is a right angle Proof: Since AB is a diameter of the circle, the midpoint of AB must be the center of the circle. Denote the center by O. Then 0 = 0B a OC by (Justification 1). By the (Justification 2) we have LOAC = LOCA and LOBCA LOCB. Let = N(COAC) and 8 - (LOBC). Then 2a + 28 180"...
Problem 1-4. Let AABC be a right triangle with hypotenuse AB. Suppose that D, E, F e AB, BF ZACB. Prove that ZDCE ZECF. FA, ZBDC is a right angle, and CE is the bisector of В E 14 F onu Rnonocitions 1.31 on these-but be sure to label what IT.
ΔΑΒΟ-withA(-5,2), B(-3,3), and C-1,Ok ΔDEF WRh D(3-0). E(5,1 ), and F07,-2); Prove: AABC ADEF Read the following proof for this protlem carefully, and then follow the directions with A , B-3,3), and C(-1.0 Fwith DX3.0,ES,1), and FO.-2 B-5and DE Match the numbered blanks with the phrases, words, expressions, or statemenits that correctily ill in the corresponding blanks in the proaf blank t blank 2 Distance forrmula blank 3 Transtive Property of Equality blank 4 AC- V20 and DF- blank 5...
Additional problem 1 Let AABC be a triangle, let be the bisector of the angle ZCAB Let P be the intersection of and BC. Let R be the point on the line AB such that AR-AC, and let X-APnRC. Let Q denote the intersection point between the line through B and X and AC. (a) Show that the triangle AARC is isosceles, and deduce that RX-XC. (b) Apply Menelaus's theorem to the triangle AARC with the line through B, X,...
SWI. U 7. Consider the right triangle AABC with the right angle 2C = 90° and sides c = 10 cm, a = 8 cm, b = 6 cm. If angle LA is opposite to side a, find sin A,cos A, tan A, cot A, sec A, CSC A.