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Last updated 3:46 AM on 3/6/23
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25 Terms
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postulates
statement that u just know
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postulates
on a flat plane, parallel lines never meet
a straight line is 180
all right angles are congruent
a straight line is 180
all right angles are congruent
3
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transitive
* a special case of substitution
* if a=b and b=c then a=c
* if a=b and b=c then a=c
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substitution
* if A + B = C + D and B = E then A + E = C + D
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addition/subtraction property
* a+b=c or c-b=a etc.
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vertical angels are congruent
vertical angels are congruent
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a triangle equals 180
a triangle equals 180
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straight line = 180
straight line = 180
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if a ray/segment/line bisects an angel, it creates 2 congruent angles
if a ray/segment/line bisects an angel, it creates 2 congruent angles
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if angles form a linear pair, they are supplementary
if angles form a linear pair, they are supplementary
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if 2 angles are supp to congruent angles, they are congruent to each other
if 2 angles are supp to congruent angles, they are congruent to each other
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if 2 angles are comp to congruent angles, they are congruent to each other
if 2 angles are comp to congruent angles, they are congruent to each other
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if 2 lines are parallel, then corresponding/ alternate interior/ alternate exterior angles are congruent
if 2 lines are parallel, then corresponding/ alternate interior/ alternate exterior angles are congruent
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if 2 lines are parallel, then same-side interior/ same side exterior angles are supp
if 2 lines are parallel, then same-side interior/ same side exterior angles are supp
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if corresponding/ alternate interior/ alternate exterior angles are congruent, then 2 lines are parallel
if corresponding/ alternate interior/ alternate exterior angles are congruent, then 2 lines are parallel
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if same-side interior/ same side exterior angles are supp, then 2 lines are parallel
if same-side interior/ same side exterior angles are supp, then 2 lines are parallel
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reflexive property
a number /angle/side is equal to itself
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in a triangle two angles opposite two congruent sides are congruent angles
in a triangle two angles opposite two congruent sides are congruent angles
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side splitter theorem
if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally
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angle bisector theorem
if a ray bisects the angle of a triangle, it divides the opposite side into segments that are proportional to the adjacent sides
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SSS postulate
if three angles of one triangle are congruent to the corresponding angles of the other triangle, then the triangles are similar
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AA theorem
if two angles of one triangle are congruent to the corresponding angles of the other two, then the triangles are similar
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SSS theorem
if the ratios of the measures of corresponding sides are equal, then the triangles are similar
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SAS similarity theorem
if the ratios of the measures of two pairs of corresponding sides are equal and the included angles are congruent, then the triangles are similar
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corresponding sides and angles in similar polygons
* the corresponding sides of the triangle are proportional
* corresponding angles of the triangles are congruent
* corresponding angles of the triangles are congruent