Math / Geometry

Question20) Classify the triangle by congruence. isosceles scalene adjacent equilateral vertical 21) Classify the triangle by angle measure. complementary right acute supplementary

Studdy Solution

STEP 1

1. We are given a triangle $\triangle HJK$ .
2. We need to classify the triangle by congruence and by angle measure.
3. The sides of the triangle are labeled as $HJ = 2a$ , $JK = 4a - 29$ , and $HK = 2a$ .
4. The angle $\angle J = 65^\circ$ .

STEP 2

1. Classify the triangle by congruence.
2. Classify the triangle by angle measure.

STEP 3

To classify the triangle by congruence, compare the lengths of the sides. We have:
- $HJ = 2a$ - $JK = 4a - 29$ - $HK = 2a$
Notice that $HJ = HK$ , which means two sides are equal. This indicates that the triangle is isosceles.

STEP 4

To classify the triangle by angle measure, we need to consider the given angle and the properties of triangles. We know:
- $\angle J = 65^\circ$
Since no angle is given as $90^\circ$ or greater, we need to determine if the triangle is right, acute, or obtuse. We know:
- An acute triangle has all angles less than $90^\circ$ . - A right triangle has one angle equal to $90^\circ$ . - An obtuse triangle has one angle greater than $90^\circ$ .
Given $\angle J = 65^\circ$ , and without further information suggesting a $90^\circ$ angle, we can assume the triangle is acute.
The triangle $\triangle HJK$ is classified by congruence as isosceles and by angle measure as acute.

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