geometry a - unit 3: segments, lines, and angles lesson 12-15

lines m and n are parallel lines cut by a transversal l. which answer gives statements that should be used to prove angles 2 and 8 are congruent?

angles 2 and 4 are congruent as vertical angles; angles 4 and 8 are congruent as corresponding angles.

use the figure to answer the question. for △abc, ac ≅ ab which set of measures is possible for ∠cab and ∠cba?

m∠cab = 30, m∠cba = 30

lesson 14

perpendicular bisectors

in the following figure, ba ≅ ca, and d is on bc. if bd = 3, then cd = blank

3

a triangle has two congruent sides. which answers list possible types of angles for this triangle? select two that apply

1 right angle and 2 congruent acute angles 1 obtuse and 2 angles with the same measure of 40.

use the figure and information to complete the proof. given: ab ≅ cb, bd bisects ∠abc prove: m∠1 = m∠2 match each numbered statement in the proof with the correct reason.

1. ab ≅ cb, bd bisects ∠abc : given 2. ∠3 ≅∠4 : definition of angle bisector 3. BD≅ BD : reflexive property of congruence 4. abd ≅ cbd : sas congruence postulate 5. ∠1 ≅∠2 : corresponding parts of corresponding triangles are congruent. 6. m∠1 = m∠2 : definition of congruent angles

use the figure to complete the sentence. if line e is the perpendicular bisector of bc, and bd = 2, then cd = blank

2

in triangle abc, ca = 2, cb = 2, m∠a = a∘, and m∠b = b∘ which are the possible values of a and b?

a = 45 b = 45

lesson 15

segments in triangles

use the following figure and information to complete the proof. given: m∥n line l is a transversal of lines m and n prove: ∠3≅∠5 match each numbered statement in the proof to its correct reason.

1. m∥n line l is a transversal of lines m and n : given 2. ∠3 and ∠1 are vertical angles : definition of vertical angles 3. ∠3 ≅∠1 : vertical angles theorem 4. ∠1 and ∠5 are corresponding angles : definition of corresponding angle 5. ∠1 ≅∠5 : corresponding angles postulate 6. ∠3≅∠5 : transitive property of congruence

use the figure and information to complete the proof. given: de and df are midsegments of △abc prove:∠edf ≅∠dfb match each statement in the proof with the correct reason.

1. de and df are midsegments of △abc : given 2. de is parallel to bc : triangle midsegment theorem 3. ∠edf and∠dfb are alternative interior angles : definition of alternative interior angles 4. ∠edf ≅∠dfb : alternative interior angles theorem

in the following figure, ba is a perpendicular bisector of dc. if bd = 3.7 units and ac = 4.1 units, what is the length of bc?

3.7

use the figure to answer the question. allison drew a map of where she and her friends live. allison's house is at point a, and her friends live at points b, c, and d. she only wrote some of the distances, in blocks, on the map. also, ad is a perpendicular bisector of bc. allison wants to know the distance between her house and point c. what is the measure of ac?

4.24

use the figure and information to complete the proof. given: m∥n prove: m∠1 + m∠2 + m∠3 = 180∘ match each numbered statement in the proof with the correct reason.

90% 1. m∥n : given 2. m∠1 + m∠5 = m∠abe : angle addition postulate 3. ∠abe and ∠4 are a linear pair : definition of linear pair 4. m∠abe + m∠4 = 180 : linear pair postulate 5. m∠1 + m∠5 + m∠4 = 180 : substitution property of equality 6. ∠2 and ∠4 are alternative interior angles, ∠3 and ∠5 are alternative interior angles : definition of alternative interior angles 7. ∠2 ∠4, ∠3 ∠5 : alternative interior angles theorem 8. m∠2 = m∠4, m∠3 = m∠5 : definition of congruent angles 9. m∠1 + m∠3 + m∠2 = 180 : substitution property of equality 10. m∠1 + m∠2 + m∠3 = 180 : commutative property of addition

lines m and n are parallel lines cut by a transversal l. which answer gives statements that should be used to prove angles 1 and 6 are supplementary angles?

angles 1 and 2 form a linear pair; angles 2 and 6 are congruent as corresponding angles.

use the following figure and information to complete the proof. given: m∠4 + m∠5 = 180 prove: m∥n match each numbered statement in the proof to its correct reason.

1. m∠4 + m∠5 = 180 : given 2. ∠4 and ∠5 are supplementary angles : definition of supplementary angles 3. ∠4 and ∠5 are same-side interior angles : definition of same-side interior angles 4. m∥n : converse of the same-side interior angles theorem

use the figure and information to complete the proof. given: m∥n prove: m∠3 + m∠6 = 180 match each numbered statement to the correct reason in the proof.

1. m∥n : given 2. ∠3 and ∠6 are same-side interior angles : definition of same-side interior angle 3. ∠3 and ∠6 are supplementary : same-side interior angles theorem 4. m∠3 + m∠6 = 180 : definition of supplementary

in triangle abc, cd is a median. the area of △acd =24 cm2 the area of △bcd is equal to _[blank]_ cm2 because _[blank]_.

24 the median connects vertex c to the midpoint of ab.

use the figure to answer the question. △abc has a right angle, ∠abc, and m∠bca = 45. therefore, m∠cab = [blank]

45 + 90 + cab = 180 135 + cab = 180 cab = 45

use the diagram and information to complete the proof. given: ad is the perpendicular bisector of bc prove:∠b ≅ ∠c match each numbered statement with the correct reason in the proof.

75% 1. ad is the perpendicular bisector of bc : given 2. ab = ac, db = dc : perpendicular bisector theorem 3. ab ≅ ac, db ≅ dc : definition of congruent triangles 4. ad ≅ ad : reflexive property of congruence 5. abd ≅ acd : definition of congruent segments 6. ∠b ≅ ∠c : sss congruence postulate

use the following information to complete the proof. given: ac ≅ ad, ab is a median of cd. prove: △abc ≅△abd match each statement in the proof to the correct reason.

1. ac ≅ ad, ab is a median of cd : given 2. bc ≅ bd : definition of median 3. ab ≅ ab : reflexive property of congruence 4. △abc ≅△abd : sss congruence postulate

lesson 13

angles in triangles

klaus's house is located at point k, and his friend genny's house is located at point g. the public library and science museum, which they often visit together, are located at point l and m, respectively. klaus and genny think that the library is the same distance from both of their houses and that the museum is the same distance from both of their houses. which statement proves their assumptions?

the street with the library and museum crosses the street with the houses at a 90 angle and is equidistant from both houses.

examine triangle prs if m∠spr = 65 and m∠prs = 51, then m∠pst = [blank]

116

use the figure and information to complete steps 6 through 10 in the proof. given: m∥n prove: m∠1 + m∠2 + m∠3 = 180 match each numbered statement in the proof with the correct reason.

6. ∠2 and ∠4 are alternative interior angles, ∠3 and ∠5 are alternative interior angles : definition of alternative interior angles 7. ∠2 ∠4, ∠3 ∠5 : alternative interior angles theorem 8. m∠2 = m∠4, m∠3 = m∠5 : definition of congruent angles 9. m∠1 + m∠3 + m∠2 = 180 : substitution property of equality 10. m∠1 + m∠2 + m∠3 = 180 : commutative property of addition

which answer choices give enough information to determine all three angle measures of an isosceles triangle? select all that apply

a triangle with an obtuse angle of 124, a triangle with an angle of 90

the following design shows a structure that supports the roof of a house. it is in the shape of a triangle. if ab = 8.2 feet, bd = 6 feet, cd = 6 feet, and m∠adc = 90, which figure is a perpendicular bisector of abc?

ad

in the following figure, ac = 4 units and cb = 4 units. which statements are true? select all that apply

ae = eb m∠aed = 90

lines m and n are parallel lines cut by a transversal l. https://cdstools.flipswitch.com/asset/media/1157380 which answer gives statements that should be used to prove angles 1 and 7 are congruent?

angles 1 and 3 are congruent as vertical angles; angles 3 and 7 are congruent as corresponding angles.

lesson 12

angles and parallel lines

lines m and n are parallel lines cut by a transversal l. which statements should be used to prove angles 1 and 8 are supplementary angles?

angles 1 and 4 form a linear pair; angles 4 and 8 are congruent as corresponding angles.

use the figure to complete the sentences. in △abc, ad ≅ db, ae ≅ ec, de = 4 cm, and de is a _[blank a]_. therefore, bc = [blank b]

a: midsegment b: 8 cm

lines m and n are parallel lines cut by a transversal l. which angle pair relationship should be used to prove lines m and n are parallel?

angles 1 and 5 are congruent corresponding angles.

lines m and n are cut by a transversal l. which angle pair relationships should be used to prove lines m and n are parallel?

angles 3 and 6 are supplementary same-side interior angles.

use the diagram to answer the question. if it is given that ab ≅ cb, how can it be proved that m∠a = m∠c?

draw an angle bisector from b to a point d such that d is on ac. then, show that corresponding sides and the angle between these sides of new triangles abd and cbd are congruent. finally, use the side-angle-side congruence postulate and the definition of congruent angles to show m∠a = m∠c.

isha constructs the wood frame of a paper kite. she crosses two sticks as shown in the following figure. she wants to connect the sticks so that the edges of the paper have certain measurements. she wants km = kn and ml = nl. how should she position the sticks?

place kl at a right angle on mn so it bisects mn

use the figure and information to complete the proof. given:∠3≅∠5 prove: m∥n match each numbered statement with the correct reason in the proof.

1. ∠3≅∠5 : given 2. ∠3 and ∠5 are alternative interior angles : definition of alternative angles 3. m∥n : converse of the alternate interior angles theorem