Angle Bisectors and the Incenter: Practice Level 1 | Geometry

Level 1 · Foundational 0 / 12 answered

Question 1 of 12

1

PX is perpendicular to line $\ell$ and X lies on $\ell$ . PX is 8 cm. A slanted segment PY reaches another point Y on $\ell$ and is 10 cm. What is the distance from P to $\ell$ ?

Answer choices for question 1 A 2 cm B 8 cm C 10 cm D 18 cm
2

P is on the internal bisector of angle UOV. PX and PY are perpendiculars to the two side lines. If PX is 8.5 cm, what is PY?

Answer choices for question 2 A 4.25 cm B 17 cm C It cannot be determined D 8.5 cm
3

Which lines meet at a triangle's incenter?

Answer choices for question 3 A The three internal angle bisectors B The three perpendicular bisectors of its sides C Three lines through the vertices chosen at random D The three side lines
4

I is the incenter. F is the perpendicular foot on a side. IF is 3 cm, while a segment from I to a vertex is 9 cm. What is the inradius?

Answer choices for question 4 A 6 cm B 9 cm C 3 cm D 12 cm
5

P lies on an internal angle bisector and X,Y are the perpendicular feet. Which facts prove triangles OXP and OYP congruent by AAS?

Answer choices for question 5 A Two right angles alone B Equal lengths OU and OV for any points U,V on the rays C Their right angles, their equal angles at O, and common side OP D The fact that P is inside the angle alone
6

An arc centered at O meets two side rays at U and V. Why is OU equal to OV?

Answer choices for question 6 A They are radii of the same circle B U and V must be the same point C Every two sides of an angle have equal length D OX is perpendicular to UV
7

P is strictly inside an angle less than 180 degrees. Its perpendicular distances to the two side lines are equal. What follows?

Answer choices for question 7 A P is the midpoint of UV for any U,V on the rays B OP is perpendicular to both rays C The whole angle must be a right angle D OP lies on the internal angle bisector
8

The perpendicular from P to the supporting line AB lands beyond B. Which length measures the distance from P to line AB?

Answer choices for question 8 A PA in every case B The length from P to that perpendicular foot C PB in every case D AB
9

Where is the incenter of an obtuse triangle?

Answer choices for question 9 A Strictly inside the triangle B At the obtuse vertex C On the longest side D Outside across the longest side
10

Ray BR internally bisects an angle measuring $62^\circ$ . What is either half-angle?

Answer choices for question 10 A $28^\circ$ B $62^\circ$ C $31^\circ$ D $124^\circ$
11

The incircle of triangle ABC has center I, and IF is perpendicular to side AB at F. How many points does the incircle share with side AB?

Answer choices for question 11 A No points B Exactly one point, F C Exactly two points, A and B D Every point of AB
12

Which comparison belongs to the incenter theorem?

Answer choices for question 12 A Equal distances to all three vertices B Equal distances to every point on each side C Equal lengths of all three sides D Equal perpendicular distances to all three side lines