2. Suppose that T, U, and V are the points where the incircle of AABC touches the sides BC, AC, and AB, respectively. Show that the cevians AT, BU, and CV are concurrent.

Q: 4. State and prove synthetically the converse of the angle bisector theorem. B P E C

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Q: Consider points P, Q, R, and S. Suppose that u =PQ, v = QR, -59 u = RP, and 52 v = PS. a) Are P, Q,…

A: We are given points P,Q,R,S such that   u=PQ→, v=QR→, -59u=RP→, 52v=PS→ Also find order of points on…

Q: Points A, B, C, and D are collinear and positioned in that order. Find the length indicated. 8) Find…

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Q: In Figure 4.36, AB || DC and AD = BC. a) Find the measures of the angles of ABCD if mZA = 12x + 30…

A: a) ABCD is an isosceles trapeziam. So we have ∠D=∠C=z (say). We know that ∠A and ∠D are…

Q: Find a positive and a negative coterminal angle for each given angle. T 5) 29t 18 6) 2

A:

Q: 2. Let ABCD be a quadrilateral. Let E, F, G, and H be the midpoints of its sides (as shown). Assume…

A: We have to use the Midpoint theorem:  "The line segment in a triangle joining the midpoint of two…

Q: O Let t- ,=<8, 4) and -8,4) and w = -6î - 2. Find: %3D a) ū + ☆ Caleulate the angle between i and T.

A: Given:

Q: 4) If point C is in the center of the base of the pyramid, find the length of line AC. A C 10 cm В 5…

A: Base of the pyramid is a square with side 5 cm.              Let find the diagonal of the square…

Q: 2. Given: ABCD is a parallelogram, DE I AF, and CF 1 AF Prove: DE = CF D C Statement Reason A E

A:

Q: 7. Given ả = [4,7, 1] and b = [−3,1, 5]: a) Calculate the angle between å and b. b) If = [3, 4, t],…

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Q: In parallelogram OAUB, OA = a and OB = b. Let OM where P is on the line segment MB. a Prove that P…

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Q: Consider the statement: (SSSS) Let ABCD and A'B'C'D' be quadrilaterals, and suppose that AB = A'B',…

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Q: 3. Use a triangle congruence postulate to prove the triangles below congruent. Write a two-column…

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Q: In △ABC, AB = 5, BC = 6, and CA = 7. E and F are points on sides AC and AB, respectively so that AF…

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Q: Point P is on segment AB such that AP:PB is 4:5. If A has coordinates (4,2), and B has coordinates…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.