Triangle ABC is a right triangle. Point D is the midpoint of side AB, and point E is the midpoint of side AC. The measure of angle ADE is 68°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 22°: Measure of angle ADE is 68° Given Measure of angle DAE is 90° Definition of right angle 3. _____ 2. _____ Measure of angle ECB is 22° Substitution property Segment DE joins the midpoints of segment AB and AC Given Segment DE is parallel to segment BC Midsegment theorem Angle ECB is congruent to angle AED 1. _____ Which statement and reason can be used to fill in the numbered blank spaces? 1. Corresponding angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 22° 1. Corresponding angles are congruent 2. Base Angle Theorem 3. Measure of angle AED is 68° 1. Alternate interior angles are congruent 2. Triangle Sum Theorem 3. Measure of angle AED is 22° 1. Alternate interior angles are congruent 2. Triangle Angle Sum Theorem 3. Measure of angle AED is 68°
Added by Thomas D.
Close
Step 1
The statement should be about the measure of angle AED. Since angle ADE is 68° and angle DAE is 90° (as it's a right triangle), we can use the Triangle Sum Theorem (the sum of the angles in a triangle is 180°) to find that the measure of angle AED is 22°. Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 65 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Triangle ABC is a right triangle. Point D is the midpoint of side AB and point E is the midpoint of side AC. The measure of angle ADE is 36°. The following flowchart with missing statements and reasons proves that the measure of angle ECB is 54°: Which statement and reason can be used to fill in the numbered blank spaces? A. Measure of angle AED is 36° Base angle theorem Corresponding angles are congruent B. Measure of angle AED is 54° Base angle theorem Alternate interior angles are congruent C. Measure of angle AED is 54° Triangle Sum Theorem Alternate interior angles are congruent D.Measure of angle AED is 54° Triangle Sum Theorem Corresponding angle are congruent
Danielle F.
In ΔABC shown below, ∠BAC is congruent to ∠BCA: Triangle ABC, where angles A and C are congruent. Given: Base ∠BAC and ∠ACB are congruent. Prove: ΔABC is an isosceles triangle. When completed (fill in the blanks), the following paragraph proves that Line segment AB is congruent to Line segment BC making ΔABC an isosceles triangle. Construct a perpendicular bisector from point B to Line segment AC. Label the point of intersection between this perpendicular bisector and Line segment AC as point D: m∠BDA and m∠BDC is 90° by the definition of a perpendicular bisector. ∠BDA is congruent to ∠BDC by the definition of congruent angles. Line segment AD is congruent to Line segment DC by the definition of a perpendicular bisector. ΔBAD is congruent to ΔBCD by the Angle-Side-Angle (ASA) Postulate. Line segment AB is congruent to Line segment BC because corresponding parts of congruent triangles are congruent (CPCTC). Consequently, ΔABC is isosceles by definition of an isosceles triangle.
Supreeta N.
In ΔABC shown below, BD/BA = BE/BC: Triangle ABC with segment DE intersecting sides AB and BC respectively. The following flowchart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side: Top path, by Given: BD/BA = BE/BC. By Side-Angle-Side Similarity Postulate, triangle ABC is similar to triangle DBE. By space labeled by 2, space labeled by 1 occurs. By Converse of the Corresponding Angles Postulate, line segment DE is parallel to line segment AC. Bottom path, by Reflexive Property of Equality, angle B is congruent to angle B. By Side-Angle-Side Similarity Postulate, triangle ABC is similar to triangle DBE. By space labeled by 2, space labeled by 1 occurs. By Converse of the Corresponding Angles Postulate, line segment DE is parallel to line segment AC. Which reason can be used to fill in the numbered blank space? 1. ∠BDE ≅ ∠BAC 2. Corresponding Angles Postulate 1. ∠BDE ≅ ∠BAC 2. Corresponding Parts of Similar Triangles 1. ∠BDE ≅ ∠BCA 2. Alternate Exterior Theorem 1. ∠BDE ≅ ∠BCA 2. Corresponding Parts of Similar Triangles
Allison K.
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD