Identify the two triangle congruence criteria that do not guarantee congruence. explain why they do not guarantee congruence, and provide illustrations that support your reasoning.

Hello mate!

there are two congruence criteria that do not guarantee congruence:

AAA ( or 3 angles)

two triangles can have the same 3 angles, but different size, then they are not congruent; an example of this is:

take the triangle rectangle of both cathetus = 1 and hypotenuse = √2, where the angles are 90°, 45° and 45°

and now take the triangle rectangle with both cathetus = 2 and hypotenuse = √8, this triangle also has the angles 90°, 45°, and 45°, so this two triangles succeed the AAA criteria, but are not congruent.

SSA (side-side-angle)

If two triangles satisfy the SSA  criteria and the corresponding angles are acute and the length of the side opposite to the angle is greater than the length of the adjacent side multiplied by the sine of the angle (but less than the length of the adjacent side), then the two triangles are not necessarily congruent.

This is kinda harder to illustrate;  

think on a triangle rectangle where you have the measure of both cathetus and one of the angles different from 90° as the SSA data.

and now think on another triangle that has the same adjacent cathetus and angle, and where the other cathetus is rotated (in a sense where 90° is decreasing) to the point where its tip intercepts the hypotenuse of the first triangle.

Those two triangles meet the SSA criteria but are not congruent.

the diameter is 16 cm. are you a teacher?

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.